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Digitized  by  tine  Internet  Archive 

in  2010  with  funding  from 

NCSU  Libraries 


http://www.archive.org/details/cottonspinningcaOOwint 


COTTON   SPINNING    CALCULATIONS 
AND  YARN    COSTS 


COTTON    WEAVING    AND    DESIGNING.     By 

John  T.  Taylor,  late  Lecturer  on  Cotton  Weaving  and 
Designing  in  the  Preston  and  other  Technical  Schools. 
Revised  under  the  direction  of  F.  Wilkinson,  Director  of 
the  Textile  and  Engineering  School,  Bolton.  With  402 
Diagrams,     Crown  Svo,  "js.  6d,  net. 

THE    ELEMENTS    OF   COTTON    SPINNING. 

By  John  Morris  and  F.  Wilkinson.  With  a  Preface 
by  Sir  B.  A.  Dodson,  C.E.,  M.I.M.E.  With  169  Diagrams 
and  Illustrations.     Crown  8vo,  "js.  6d. 

PRINCIPLES  OF  WORSTED  SPINNING.     By 

Howard  Priestman.  With  118  Illustrations.  Svo, 
7^.  6d.  net. 

WILD  AND  CULTIVATED  COTTON  =  PLANTS 

OF  THE  WORLD  :  a  Revision  of  the  Genus  Gossypium, 
framed  primarily  with  the  object  of  aiding  Planters  and 
Investigators  \\  ho  may  contemplate  the  Systematic  Improve- 
ment of  the  Cotton  Staple.  By  Sir  George  Watt, 
C.I.E.,  M.B„  CM.,  LL.D.  (Abd.  and  Glasg.),  F.L.S., 
formerly  Professor  of  Botany,  Calcutta  University,  and 
Reporter  on  Economic  Products  to  the  Government  of 
India.  With  53  Plates,  9  of  which  are  Coloured.  Royal 
Svo,  30i".  net. 

JACQUARD    WEAVING     AND     DESIGNING. 

By  F.  T.  Belt.,  Medallist  in  Honours  and  Certificated 
Teacher  in  "  Linen  Manufacturing"  and  in  "Weaving  and 
Pattern  Designing,"  City  and  Guilds  of  London  Institute. 
^^'ith  199  Diagrams.     Svo,  12^.  net. 

LONGMANS,   GREEN,  AND    CO. 

LONDON,  NEW  YORK,  BOMKAY,  AND  CALCUTTA 


COTTON  SPINNING  CALCULATIONS 
AND  YARN  COSTS 

A   PRACTICAL   AND   COMPREHENSIVE    MANUAL   OF 

CALCULATIONS,   YARN   COSTS,   AND   OTHER 

DATA  IN\'OLVED   IN   ADAPTING   THE 

MACHINERY  IN   ALL  SECTIONS,    AND  FOR  ALL  GRADES, 

OF  SPINNING  AND  DOUBLING 


JAMES   WINTERBOTTOM 

LECTURER    IN    COTTON    SPINNING,    MUNICIPAL   SCHOOL   OF   TECHNOLOGY,    MANCHESTER 


LONGMANS,    GREEN,    AND    CO. 

39  PATERNOSTER  ROW,  LONDON 

NEW  YORK,  BOMBAY,  AND  CALCUTTA 

1907 

All  rights  reserved 


PREFACE 

The  aim  of  the  author  of  this  work  has  been  to  provide  the 
student  with  particulars  of  the  gearing  in  all  the  machines 
involved  in  Cotton  Spinning,  together  with  a  method  of  calcu- 
lating the  trains  of  gearing.  These  are  accompanied  by  suitable 
examples  and  exercises. 

Existing  works  containing  Spinning  Calculations  appear  to 
deal  with  this  subject  in  a  manner  too  abstract  for  the  average 
student.  In  this  book  the  details  connected  with  the  calcu- 
lations and  essential  in  changing  the  conditions  of  working,  are 
fully  given. 

The  effects  of  twist  in  yarn  are  introduced  in  consideration 
of  its  importance  and  in  the  hope  of  stimulating  further  investi- 
gation of  its  working. 

The  yarn  costs  are  dealt  with  particularly  to  assist  students 
preparing  for  the  City  and  Guilds  of  London  Institute  examina- 
tions in  Cotton  Spinning. 

MANCHESTER,  ^^,^      ^   \      )  ' 

Aurjust,  1907.  \         J    \ 


^^ 


UBRABY  01? 
K.  Ci  STATE  COIiliB^MB 


S5I5 


CONTENTS 


TRANSMISSION   OF   MOTION 

PAGE 

Ascertaining    the    rate— Direction — Sizes — Effects   of    changes — Examples 

and  exercises 1 — 15 


COTTON   MIXING 

Bale-breakers  or  cotton  pullers  and  distributors — Their  object — Types — 
Actions — Capacities — S^ieeds — Drafts — Merits  and  demerits — Examples 
and  exercises — Notes  on  the  stack  and  direct  niethods        ....     15 — 25 


OPENING  AND   SCUTCHING 

Openers — Gearing — Speeds— Methods  of  feeding — Drafts — Lap  weight — Ex- 
amples and  exercises — Scutchers — The  gearing — Speeds — Drafts — Lap 
weight— Production — Lap  length  motions — Changes  in  speed,  weight, 
and  cotton — Examples  and  exercises — Positive,  semi-,  and  non-positive 
draft  connections — Non-stop  working — Controlling  factors— Speed  of 
beaters  and  fans — Sizes  of  feed  rollers — Overscutching  and  other  defec- 
tive treatment 25 — 56 


CAEDING 

Cards— The  gearing— Speeds— Drafts— Alterations— Functions  of  parts- 
Conditions  controlling  efficiency — Rate  of  movement  of  flats — Wrapping 
— Names  applied  to  cotton  in  the  processes — Counting  cotton — Card 
clothing,  counting,  preparation  for  mounting,  character  of  its  points — 
Examples  and  exercises 56 — 76 

PREPARATION   FOR,   AND   COMBING 

Sliver   lap   machine — Object — Names   and   functions   of  parts — Gearing — 

Speeds — Drafts — Production — Examples  and  exercises      ....     76 — 80 

Ribbon  lap  machine — Object — Names  and  functions  of  parts — Gearing — 

Speeds — Drafts — Production — Examples  and  exercises      ....     80 — 84 


VUl  CONTENTS 

PAGE 

Combing  —  Alternative  preparation  of  laps  —  Objects  of  combing  —  The 
Nasmith  comber  —  Speeds  —  Drafts,  and  the  limitations  in  range  — 
Weights  of  sliver  and  waste — Examples  and  exercises 84 — 95 

The  Heilmann  comber — Differences  of  the  duplex  and  Nasmith^ — Speeds — 
Drafts — Attaching,  how  adjusted — Draft  restrictions — Items  controlling 
the  efficiency — Examples  and  exercises 95 — 102 

ATTENUATING  AND   EQUALIZING   (THE 
DRAWING   PROCESS) 

The  draw-frame — Objects — Number  of  heads  useful — -Object  and  mode  of 
testing  slivers — System  of  "  putting  up  " — Allocating  the  drafts — 
Spacing  the  sliver — Speeds,  drafts,  counts  and  production — Suitable 
sizes  of  rollers — Analysis  of  systems  of  roller  gearing — The  arrangement 
of  heads — A  mode  of  ascertaining  the  total  draft — Examples  and 
exercises 102 — 110 


ATTENUATING   (THE  FLY-FRAME  PROCESSES) 

The  objects  of  the  fly  frames :  slubber,  intermediate,  rover  and  jack — The 
necessity  for  repetition— The  object  of  twisting — The  direction  of  twist- 
ing, its  influence  —  Twist  constants  —  The  gearing  in  these  frames  — 
The  names  and  functions  of  parts — Effects  of  altering  the  cone  train — 
Changes  in  speed,  draft,  count,  twist  and  spacing  —  Examples  and 
exercises — Cone  drums  and  differentials — Reasons  for  a  differential  train 
of  fixed  value 110—141 

Analysis  of  the  action  of  drawing  rollers  with  deductions    ....       152 — 154 

SPECIFICATION   OF   CONDITIONS   IN   CARDING 
DEPARTMENT 

Suitable  counts  and  spindle  speeds — "Preparation"  defined — Counts  practi- 
cable with  the  available  machinery — Factors  controlling  the  allocation 
of  the  total  draft — Examples  and  exercises — Hank  indicators 

141—152,  154—156 

Full  bobbin  measuring  motions 156 


SPINNING 

The  mule — Description  and  functions  of  parts — Twist  constants — Factors 
controlling  the  value  of  all  trains — Examples  of  speeds,  twist,  draft, 
count,  builder,  gain  and  production— Gearing  in  mules  by  Dobson  and 
Barlow,  Hetherington,  Piatt,  Trelfall  —  Jacking,  slow  roller,  double 
speed,  twisting,  hastening,  backing-off  and  taking-up  and  other  motions 
— Comparison  of  actual  speeds  and  productions  with  calculated — Losses 
in  driving — Use  of  the  tachometer  and  tachoscope — Hank  and  other 
indicators — Tables  of  productions 156 — 204 


CONTENTS  IX 

PAGE 

The  ring  frame  —  Geariug  — Speeds— Draft— Twist  and  other  changes— 
Examples  and  exercises — Comparison  of  calculated  with  actual  speeds 
and  productions— Losses  in  driving — Table  of  productions— Conditions 
favourable  to  ring  spinning— The  influence  of  twist  on  the  output      204—213 


YARNS 

Twist  standards  for  single— Effects  of  twist  in  single— Relative  breaking 

resistance  in  single 214     216 

Twist  standards  for  various  kinds  of  folded  yarns— The  influence  of  the 
direction  and  extent  of  twist  in  the  singles  upon  the  strength  and  other 
features  of  the  folded  yarn— The  aims  of  doubling— Equilibrium  in 
folded  yarns— Features  developed  in  folding— To  ascertain  the  suitable 
twist 216—224 


DOUBLING 

The  ring  doubling  frame— Gearing— Speeds— Twist-production— Examples 
and  exercises— The  twiner  mule— Gearing — Speeds— Twist-production 
— Examples  and  exercises 224 — 230 

Winding— Keeling 247—249 


COSTS   OF  YARN 

Total  and  details  of  expenses— Examples  of  costing— Comparison  of  cost- 
Yarn  from  single  and  double  roving — Combed  qualities — Ring  yarn — 
Cotton  and  yarn  price  lists — Cost  of  power  space— Power  required- 
Extra  cost  of  combing — Departmental  costs 231 — 247 

INDEX 251 


COTTON  SPINNING  CALCULATIONS  AND 
COSTS  OF  YARN 


Tkansmissiox  of  Motion 

The  Method  of  calculating  the  Rate  of  Motion,  when  Tooth  Gear  is 
employed. — When  wheels  are  employed  in   a   simple  or  direct 
train,  as  in  Fig.  1,  their  move- 
ment, in  teeth  or  circumferen- 
tially,    is    alike.      Their    axial 
movement    differs    only    when 
the   wheels    are    not    alike   in 
size.     This   difference  is,  rela- 
tively,  inverse    to   their   teeth  pj^  j 
contents.     This    is   proved    by 

assuming  that  the  wheels  A,  B,  C,  and  D  in  Fig.  1  contain 
100,  75,  50,  and  25  teeth,  respectively,  and  that  the  first 
mentioned  moves  one  revolution.  Thus,  the  wheel  A  moves 
to  the  extent  of  100  teeth,  and  since  its  teeth  gear  with  those 
of  B,  and  the  latter  with  C,  and  these  also  with  D,  then  each  of 
them  will  move  tooth  per  tooth  of  A,  and  therefore  each  will 
move  100  teeth.  Hence,  their  respective  axial  movements  will 
be— 

A  =  lor};}|l  B  =  WorU 

C  =  JgOf  or  2  D  =  ^Si  or  4 

The  preceding  results  show  that  the  axial  movement  or  revo- 
lutions of  wheels,  under  such  conditions,  are  inversely  pro- 
portional to  their  relative  teeth  contents,  and  therefore  as 
follows  : — 

B 

fiSOmCTY  UBRARY 
mr  r  Qf^ffi  C 


COTTON   SPINNING  CALCULATIONS 


Tooth  contents. 

Ratios  of  their  revolutions. 

A 
B 

100 
75 

1 

n 

or 

75 
100 

A 

C 

100 
50 

1 

2 

or 

50 
100 

A 
D 

100 
25 

1 

4 

or 

25 
100 

B 

C 

75 
50 

1 

n 

or 

50 
75 

B 
D 

75 
25 

1 

3 

or 

25 
75 

C 
D 

50 
25 

1 
2 

or 

25 

50 

The  Direction  of  the  Movement  of  Tooth  Wheels. — In  simple 
direct  trains  of  wheels  this  is  always  respectively  alternate. 
This  is  seen  on  reference  to  Fig.  1.  By  numbering  the  wheels 
in  their  respective  numerical  order,  it  is  seen  that  those  having 
odd  numbers  will  all  rotate  in  the  same  direction,  and  reverse 
to  those  having  even  numbers. 

The  following  are  examples  in  the  application  of  the  afore- 
mentioned points  in  respect  of  Fig.  1 : — 

Example  I. — Assuming  A  revolves  100  times  per  minute,  at  what  rates 
would  B,  C,  and  D  rotate  in  that  time  ? 

Example  II. — Assuming  B  revolves  at  the  rate  of  100  per  minute,  give  the 
rates  of  A,  C,  and  D  in  that  time. 

■  Example  III.— Assuming  C  makes  100  revolutions,  how  many  would  A,  B, 
and  D  make  ? 

Example  IV. — If  D  made  100  revolutions,  how  many  would  A,  B,  and  C 
make? 


Answers — 

Example  I. — The  movement  of  A  expressed  in  teeth  per  minute  would  be 
Eevolutions  of  wheel  x  number  of  teeth  it  contains,  this  =  100  x  100,  which 


AND  COSTS   OF   YARN  3 

number  of  teeth  B,  C,  and  D  must  likewise  move,  and  therefore  the  number  of 
teeth  moved,  per  minute,  by  B  divided  by  the  number  of  teeth  which  it  contains, 
will  give  its  revolutions  in  that  time. 

.*.  =v =  133^  revolutions  per  minute  of  B 

Similarly — 

The  revolutions  per  minute  of  C  = ^^ =  200 

_-       100  X  100       ._- 
»  »  D  =  25 ^ 

Example  II. — The  number  of  teeth  which  B  moves  per  minute  =  100 
revolutions  x  75  teeth,  and  this  number  A,  C,  and  D  must  consequently  move, 
and  therefore — 

The  revolutions  per  minute  of  A  =  — ^-tctt —  =  75 

Example  III. — The  number  of  teeth  which  C  moves  are  100  x  50,  which 
number  A,  B,  and  D  must  also  move,  and  therefore — 

rvu  ^  r  f  ^       1^0  X  50       _ 

The  revolutions  or  A  =  — r^^^ —  =  oO 

„  „  D  =  15^°  =  200 

Example  IV. — The  number  of  teeth  moved  by  D  are  100  x  25,  and 
therefore  A,  B,  and  C  will  move  a  like  number  ;  therefore— 

The  revolutions  of  A  =  — ,...  "    =  25 
100  X  25  _      1 

100  X  25  _    . 
^  -  ~50 

Tlie  Relative  Rates  of  Rotation  of  the  Wheels  comprised  in  any 
Direct  Train  are  respectively  inverse  to  their  Teeth  Contents. — This 
is  seen  to  be  the  case  in  all  the  preceding  examples.     Thus  in — 


COTTON   SPINNING  CALCULATIONS 


Answer  to  Example  I. — 

A:B: 

:  100: 

;  1331, 

or 

as  1 

-n 

A:C: 

:  100: 

;200 

!> 

1 

:2 

A:D: 

:  100: 

:400 

)) 

1 

:4 

Answer  to  Example  II. — 

B  :  A: 

:100; 

:    75 

» 

n 

:  1 

B:C  : 

:100: 

;150 

>) 

1  ; 

:li 

B:D: 

:  100: 

300 

» 

1  : 

;3 

Ansiver  to  Example  III. — 

C  :A: 

:100: 

:    50 

>J 

2: 

:  1 

C:  B: 

:100: 

:   66| 

J> 

U: 

1 

C:D: 

:100; 

;200 

V 

i : 

2 

Answer  to  Example  IV. — 

D:  A: 

:  100: 

:25 

)) 

4 : 

:  1 

D:B: 

:  100: 

;33i 

}1 

3: 

1 

D:C: 

:  100: 

50 

)1 

2: 

1 

Examples  in  Respect  of  the  Direction  of  Rotation. — In  Example  I.  commence 
by  numbering  A,  1 ;  B,  2  ;  C,  3  ;  D,  4 ;  thus  A  and  C  move  in  the  opposite 
direction  to  B  and  D. 

In  Example  II.  commence  by  numbering  B,  1  ;  A,  2 ;  C,  2 ;  D,  3 ;  thus  A 
and  C  move  reverse  to  B  and  D, 

NoTK. — The  reason  for  numbering  A  and  C  the  same  is  because  that  is  their 
relative  order. 

In  Example  III.  commence  by  numbering  C,  1 ;  D,  2  ;  B,  2  ;  A,  3  ;  thus  C 
and  A  move  in  the  opposite  direction  to  D  and  B, 

In  Example  IV.  the  numbering  is  D,  1 ;  C,  2  ;  B,  3 ;  A,  4 ;  thus  D  and  B 
move  in  the  opposite  direction  to  C.  and  A. 

Direct  and  Indirect  Trains. — When  wheels  are  arranged  in  an 
indirect  train!  (composed  of  two  or  more  simple  trains),  as  con- 
tained in   Fig.   2,   the    conditions    of 
transmission  differ  from  those  obtaining 
in  direct  trains  as  contained  in  Fig.  1. 
The  difference  in  Fig.  2  consists  in 
the  wheels  B  and  C  being  united  and 
have   a   common   axis.      These   must 
therefore    revolve    together.      Motion 
from  A  to  D  is  imparted  to  the  rim 
of  B  by  that  of  A,  thence  from  the 
rim  of  B  to  its   hub,  and   thence  to 
the  rim  of  C,  and  from  this  part  to  the  rim  of  D. 

The  effects  of  B  and  C  being   so   coupled   are   that   their 


Fig.  2. 


AND   COSTS   OF   YARN  5 

movement  iu  teeth  is  only  alike  when  they  contain  the  same 
number  of  teeth.  Their  relative  movement  in  teeth  differs  in 
the  direct  ratio  of  their  teeth  contents.  Thus,  if  in  Fig.  2, 
A,  B,  C,  D  contain  40,  20,  60,  and  20  teeth  respectively — 


The  revolutions  of  A  will  be  to  those  of  B 

j»  jj  ^  j>  5>  -L^ 


20  :  40,  or  as  1  :  2 
1  :    1 
20  :  60,  or  as  1  :  3 


This  shows,  in  two  only  of  the  three  instances  that  the 
relative  rotation  is  the  inverse  of  their  dimensions,  and  hence 
the  rule,  "  revolutions  of  wheels  are  relatively  inverse  to  their 
teeth  contents,"  is  only  applicable  in  respect  of  direct  trains  of 
wheels. 

Fig.  2  is  an  indirect  train,  and  comprises  two  direct  trains 
of  wheels,  namely,  AB  and  CD.  The  effects  of  their  combination 
may  be  ascertained  by  multiplying  their  separate  values, 
together,  thus  — 

2x3  =  6 
or  the  movement  of  A  :  D  : :  1  :  6 

If  A,  therefore,  made  20  revolutions,  the  movement  of  D 
in  revolutions  would  be  20  X  6  =  120,  because  A  and  B  would 
move   20  X  40   teeth,   and   therefore    B   and   C   would    make 

20  X  40  1    , .  r^        ;i  T^  n  20  X  40  X  60   ,      ,, 

— ^ —  revolutions,  C  and  D  would  move  ^7) teeth  ; 

and  therefore  the  revolutions  of  D  would  be  — ^ ^^ —  =  120, 

ZO  X  zu 

or  the  value  of  the  train  multiplied  by  the   revolutions  of  its 

first  wheel. 

The  following  is  a  summary  of  the  foregoing  deductions  in 
respect  of — 

Direct  Trains  of  Wheels. — 1.  The  circumferential  or  teeth  rate 
of  the  movement  is  alike  in  all  the  wheels  comprised  in  a  direct 
train  of  wheels. 

2.  The  rate  of  rotation  is  relatively  inverse  to  the  circum- 
ference or  teeth  contents  of  the  wheels  comprised  in  a  direct 
train. 


6  COTTON  SPINNING  CALCULATIONS 

3.  The  direction  of  rotation  is  alternate  at  each  successive 
wheel,  and  when  numbered  in  progressive  order,  the  direction 
of  the  odd-numbered  wheels  will  be  alike  and  opposite  to  those 
which  are  even  numbered. 

Indirect  Trains  of  Wheels. — 4.  The  circumferential  or  tooth 
rate  of  the  movement  is  alike  only  in  those  wheels  comprised 
in  each  of  the  several  direct  trains  which  constitute  any  indirect 
train. 

5.  The  rate  of  rotation  is  relatively  inverse  to  the  tooth 
contents  of  those  wheels  comprised  in  each  only  of  the  several 
direct  trains  of  which  the  indirect  train  is  constituted. 

6.  The  direction  of  rotation  is  alternate  at  each  successive 
wheel  in  any  one  only  of  the  several  direct  trains  which  con- 
stitute the  indirect  train. 

7.  The  direction  of  rotation  is  alternate  throughout  an  indirect 
train  when  those  wheels  which  are  fastened  to  each  other,  by  a 
shaft  or  other  coupling,  are  regarded,  when  numbering,  as  only 
one  wheel :  thus  in  Fig.  2  the  wheels  A,  B,  C,  D  would  be  num- 
bered 1,  2,  2,  3  respectively,  so  that  the  direction  of  B  and  C 
would  be  that  opposite  to  A  and  D. 

8.  The  circumferential  rate  as  well  as  the  relative  rotation, 
in  indirect  trains,  is  ascertained  by  treating  them  as  so  many 
simple  trains  as  they  may  comprise. 

Classification  of  Wheels. — When  the  function  of  a  wheel  is  to 
convey  motion  from  hub  or  axle  to  rim,  and  therefrom  to  another 
wheel,  it  is  termed  a  driver. 

When  the  motion  is  received  at  the  rim,  from  another  wheel, 
and  passes  thence  to  its  hub  or  a^le,  it  is  designated  a  driven 
wheel. 

When  the  function  of  a  wheel  is  merely  to  convey  motion 
along  its  rim  from  wheel  to  wheel,  it  is  termed  a  carrier  wheel, 
but  when  such  a  wheel  has  also  to  transmit  movement  to  its  hub 
or  axle,  for  driving  some  other  part,  it  would  also  be  termed  a 
driven  wheel,  but  only  in  respect  of  the  latter  connection. 

Examples  in  the  Classification  of  wheels  in  Figs.  1,  2,  3 — 

Fig.  1,  assuming  the  motion  flowing  from  A  to  D — 

A  is  a  driver  (motion  flowing  from  the  axle  to  rim). 


AND  COSTS  OF   YARN  7 

B  is  a  carrier  (motion  flowing  merely^along  the  rim). 

n 

^  )>  jj  )j  >> 

D  is  a  driven  (motion  flowing  from  the  rim  to  the  axle). 
If  the  motion  was  from  D  to  A  then — 

D  would  be  a  driver. 
C  ,,  carrier. 

B         „  „ 

A  ,,  driven. 

Fig.  2,  assuming  the  motion  passing  from  A  to  D — 

A  would  be  a  driver. 

B  ,,  driven  (the  motion  here  passes  to  the  axle) 

C  ,,  driver  (the  motion  here  passes  from  axle  to 

the  rim). 
D  would  be  driven. 

If  the  motion  passed  from  D  to  A  the  above  functions  would 
be  reversed. 

Fig.  3,  assuming  the  motion  passed  from  A  to  E,  and  G — 

A  to  E  :  A  would  be  a  driver. 

B        ,,  carrier. 

C         ,,  driven. 

D        ,,  driver. 

E        ,,  driven. 

A  to  G :  A  and  F  are  drivers. 

B  and  G  are  driven. 

Examples  in  respect  of  the  direction  of  rotation  with  the  motion 
as  stated  above — 

Fig.  1. — A  and  C,  their  numbers  respectively  being  1  and  3  ; 
B  and  D,  their  numbers  even  2  and  4,  their  direction  being 
opposite  to  A  and  C. 

Fig.  2. — A  and  D  the  same  direction  and  positive  (since  their 
progressive  numbers  are,  according  to  the  definition,  odd  numbers 
positive  and  even  numbers  negative) ;  B  and  C  being  numbered 
2,  2,  and  therefore  negative. 

Fig.  3. — The  numerical  order  of  A,  C,  D,  G,  is  1,  3,  3,  3 


8 


COTTON  SPINNING  CALCULATIONS 


respectively,  and  therefore  in  the  positive  direction  ;  B,  F,  E  2,  2, 
and  4  respectively,  and  therefore  negative. 

The  Method  of  calculating  the  Value  of  Wheel  Trains. — 
A  simple  method,  applicable  in  direct  or  indirect  trains, 
is  deduced  from  the  foregoing  procedure  in  ascertaining  the 
relative  movements  of  the  wheels  in  Figs.  1  and  2.  The  value 
of  the  trains,  in  each  of  those  instances,  is  found  by  multiplying 
the  sizes  of  the  driver  wheels,  in  teeth,  together  for  a  numerator, 
and  those  of  the  driven  wheels  together  for  a  denominator — 
the  resultant  being  the  value  of  the  train ;  or,  the  relation  of 


1 

4 

2 

D                            E 

5 

G 

F 

r 

3 

Fig.  3. 

the  final  wheel  in  terms  of  one  of  the  first  wheel.  This  result, 
when  further  multiplied  by  the  revolutions  of  the  first  wheel,  in  a 
given  time,  obtains  the  revolutions  of  the  final  wheel  in  that  time. 

Applying  this  in  finding  the  revolutions  per  minute  of 
shafts  2,  3,  4,  and  5  respectively,  in  Fig.  3,  when  the  sizes  of 
the  wheels  in  teeth,  alphabetically,  are  :  40,  20,  50,  25,  100,  40, 
80 ;  and  (1)  is  assumed  to  make  500  revolutions  per  minute,  the 
following  are  the  results  : — 

(1)  A  is  a  driver,  B  a  carrier,  G  is  a  driven  wheel,  and 
therefore — 

The  revolutions  per  minute  of  shaft  (2)  =  tJ]  X  500  =  400 


AND   COSTS   OF   YARN  9 

(2)  A  and  D  are  drivers,  B  is  a  carrier,  C  and  E  are  driven 
wheels,  and  hence  — 

Revolutions  of  shaft  (3)  per  miaute  =  fg  X  ,%'^o  ^  ^0^  =  100 

(3)  Here  A  is  a  driver  aad  B  the  driven  wheels,  therefore— 
|}}  X  500  =  1000  revolutions  of  shaft  (4)  per  minute 

(4)  Here  A  and  F  are  drivers,  and  B  and  G  are  driven 
wheels,  hence — 

40  .  40 
The  revolutions  of  shaft  (5)  per  minute  =  ^^    .^^  X  500  =  1333.^ 

The  Effects  of  changing  Wheels. — The  effects  of  changing  the 
size  of  any  wheel  depends  upon  its  function.  If  a  driver  wheel, 
the  axial  rate  of  all  other  wheels  receiving  motion  from  it  will  be 
altered  in  the  direct  ratio  of  the  change,  because  the  movement  of 
the  new  wheel,  in  teeth,  per  revolution,  will  be  altered  in  that 
ratio ;  and  this  will  affect  all  the  others  depending  upon  it  for 
their  motion  in  like  terms.  Hence,  changing  A  to  30,  and 
taking  the  revolutions  of  A  at  500  per  minute,  would  cause — 

The  shaft  (2)  to  rotate  at — 

500  X  g^,  by  gear;  or,, by  proportion  : 
400  X  f  g  =  300  per  minute 

The  shaft  (3)  to  rotate  at — 

500  X  |§  X  y^fpQ,  by  gear  ;  or,  by  proportion  : 
100  X  fg  =  75  per  minute 

The  shaft  (4)  to  rotate  at — 

500  X  f§,  by  gear ;  or,  by  proportion  : 
1000  X  |g  =  750  per  minute 

The  shaft  (5)  to  rotate  at — 

500  X  ?,§  X  |§,  by  gear  ;  or,  by  proportion  : 
13331  X  |g  =  ioOO  per  minute 

In  case  of  a  driven  u-liecl  hcing  altered,  the  axial  rate  of  tliose 
wheels,  dependent  upon  it  for  their  motion,  woidd  be  affected  in  the 


10  COTTON   SPINNING  CALCULATIONS 

inverse  ratio  to  that  change. — Because  the  rate  of  movement  of  its 
teeth  would  be  unaltered,  because  the  wheel  receives  its  motion 
from  the  same  wheel  as  hitherto.  Its  axial  rate  would  be 
increased  when  the  new  wheel  contains  less,  and  diminished  if 
containing  more,  teeth.  Hence,  altering  the  wheel  C  to  40  instead 
of  the  wheel  A,  assuming  the  latter  to  make  500  revolutions  i^er 
minute,  would  have  the  following  results  :  — 
Shaft  (2)  would  rotate  at — 

500  X  IJ],  or  400  X  |g  =  500  revolutions  per  minute 

Shaft  (3)  would  rotate  at — 

500  X  |£-  X  -i%\  =  125  revolutions  per  minute 

Shafts  (4)  and  (5)  would  not  be  altered. 

If  B  were  altered  to  30  instead  of  C,  then  the  following 
would  be  the  result : — 

Shaf  ts'(2)  and  (3)  would  not  have  their  speeds  affected,  because 
C  would  move  at  the  same  tooth  rate ;  thus — 

Shaft  (4)  would  rotate  at — 

500  X  II],  or  1000  X  |g  =  666§  revolutions  per  minute 
Shaft  (5)  would  rotate  at — 
500  X  *{]  X  If],  or  1333^  X  |[]  =  888|  revolutions  per  minute 

The  foregoing  show  that  increasing  the  size  of  a  driver 
wheel  increases  proportionately  the  speeds  of  the  subsequent 
wheels  in  the  train,  and  vice  versa ;  that  increasing  the  size  of 
a  driven  wheel  proportionately  decreases  the  speeds  of  the  sub- 
sequent wheels  in  the  train,  and  vice  versa.  Therefore,  to 
determine  the  teeth  contents  or  size  of  a  wheel  when  it  is  required 
to  alter  the  speeds,  the  procedure  must  be  as  follows  : — 

In  the  case  of  driver  wheels  :  the  size  of  the  wheel  it  is  decided 
to  alter,  multiplied  by  the  speed  required,  and  divided  by  the 
existing  speed,  will  give  the  wheel  required,  because  the  size 
of  this  wheel  must  be  altered  in  the  direct  proportion  of  the 
present  rate  to  the  required  rate. 

In  case  of  driven  wheels :  the  size  of  the  wheel  it  is  decided 
to  alter,  multiplied  by  the  existing  speed,  and  divided  by  required 


AND   COSTS  OF   YARN  11 

speed,  will  give  the  wheel  required,  because  the  driven  wheel 
must  be  altered  in  the  inverse  proportion  of  the  present  rate  to 
the  required  rate. 

To  determme  the  sizes  or  teeth  contents  of  wheels  to  employ  in 
a  train  in  order  to  obtain  a  specific  speed  of  the  final  wheel. 
Ascertain  the  value  of  the  train  required ;  the  distance  of  the 
shafts  apart ;  the  space  available  for  the  wheels ;  the  pitch  of 
the  teeth  that  affords  sufficient  strength,  with  due  regard  to 
lightness  ;  the  direction  of  motion.  This  latter  will  decide  whether 
the  number  of  wheels  to  employ  should  be  odd  or  even. 

The  number  of  wheels  should  be  as  few  as  possible.  The 
space  available  restricts  their  size. 

The  distance  apart  of  the  two  centres  multiplied  by 
2(3*1416)  will  give  the  sum  of  the  circumferences  of  the  wheels 
required.  This  divided  by  the  suitable  pitch  of  the  teeth  gives 
the  sum  of  their  teeth  contents,  whatever  the  number  of  wheels, 
when  they  are  arranged  with  their  centres  in  a  straight  line. 
If  their  centres  are  arranged  otherwise,  it  would  be  necessary  to 
determine  the  sum  of  their  distances  apart.  The  latter  would 
control  the  sum  of  their  teeth  contents.  The  contents  of  each 
wheel  would  then  be  decided  according  to  the  intermediate  axial 
speeds  required. 

Under  conditions  similar  to  Fig.  2,  where  the  ratio  in  the  train 
is  6  to  1 ,  and  the  latter  has  to  rotate  in  the  opposite  direction 
to  the  former,  an  odd  number  of  wheels  must  be  employed. 
The  following  would  suffice  :  A,  six  times  the  smallest  size  of  D 
practicable,  and  these  connected  by  a  suitable  carrier,  or  odd 
number  of  carriers.  If  there  is  a  wide  difference  in  the  sizes  of 
the  wheels  this  is  impracticable,  then  A,  2*4  times  B ;  and  C, 
2*5  times  D  should  be  employed. 


Exercises. — Ascertain  the  wheels  convenient  to  secure  the  undermentionecl 
values  in  the  following  trains  : — 

1.  A  direct  train  to  consist  of  six  wheels  with  axial  motion  in  the  ratios  of 
1,  2,  3,  4,  5,  and  6  respectively. 

2.  A  direct  train  to  consist  of  three  wheels  with  axial  motion  in  the  ratios  of 
1,  I,  and  3  respectively. 

3.  An  indirect  train  of  six  wheels,  comprising  three  direct  trains,  with  the 
axial  ratios  1,  1-6,  3*2,  and  8  respectively. 


12 


COTTON   SPINNING  CALCULATIONS 


4.  An  indirect  train  of  six  wheels,  comprising  three  direct  trains  with  the 
difference  in  axial  ratios  equally  distributed,  the  whole  amounting  to  8. 

5.  An  indirect  train  of  six  wheels,  the  whole  containing  a  ratio  of  1  :  9,  one 
of  the  direct  trains  to  have  the  value  2-C8. 

Rope  and  Belt  Driving. — Eopes  and  belts  are  extensively 
employed  in  the  transmission  of  motion.  The  method  of 
calculating  the  speeds  and  sizes  of  the  driving  surfaces — pulleys 
and  drums — is  identical  with  that  in  wheel  gear,  the  sizes  of 
the  pulleys  and  drums  taking  the  place  of  the  teeth  contents  in 
wheels ;  the  measurements  usual  being  in  inches  or  feet 
diameter,  these  measurements  being  made  from  diametrically 
opposite  points  of  contact  of  the  transmitting  medium. 


Fig.  4. 


Example  1  (Fig.  4). — At  what  rates  per  minute  would  B,  C,  D,  E,  F,  and 
G  rotate  if  the  gi'ooved  flywheel  of  the  engine  A  makes  50  revolutions  per 
minute,  was  25  feet,  and  the  others  5,  9,  8,  12*5,  5,  and  6  feet  respectively  ? 

Answers — 

Eevolutions  of  B  per  minute  = ;; =  300 


5 
60  X  25 


=  1601 


AND  COSTS   OF  YARN  13 

Revolutions  of  D  per  minute  = ^-^=  187'5 

_60x25_ 
"         ~      12-5     ~ 
_  60x25  _ 
"  >.         -     12-5     -^"^^ 

p  60  X  25  X  5      ,„„ 

^  "         =      12^^5^6-  =  ^^^ 

The  reasons  for  adopting  tliis  method  of  determining  the  speeds  of  parts 
when  motion  is  transmitted  by  belt  or  rope  gear  are  as  follows  :  — 

The  circumference  of  a  drum  or  pulley  or  a  circle  when  divided  by  the 
number  3-1416,  gives  its  diameter;  the  diameter  being  easier  to  measure,  it  is 
customary  to  ascertain  the  circumference  by  multiplying  the  diameter  by  that 
number.  For  practical  purposes  "/  is  considered  near  enough  in  this  kind  of 
work. 

The  rate  of  the  movement  of  the  strap  in  calculating  is  generally  assumed  to 
be  the  same  as  the  contact  surface  of  the  drum.  This,  however,  varies  con- 
siderably from  that  rate,  according  to  the  working  conditions,  such  as  tension, 
cohesiveness,  and  pHability  of  the  belt;  distances  of  the  centres  apart ;  material, 
sizes,  and  shape  of  drums;  amount  of  load.  These  are  not  usually  recognized  in 
making  calculations,  but  are  allowed  for  in  general  practice. 

The  rate  of  the  movement  of  ropes  is  about  the  same  as  the  point  of  contact 
in  well-constructed  grooved  pulleys.  In  calculating  it  is  not  customary  to  make 
an)^  allowance. 

The  rate  of  movement  of  the  ropes  engaging  with  the  grooved  flywheel  A 
will  therefore  be  the  same  as  that  of  the  pulley  at  the  centre  of  the  part  in  con- 
tact with  the  rope.  If  this  is  12*5  feet  from  the  centre  of  the  pulley,  or  equal  to 
25  feet  in  diameter,  the  circumference  of  such  a  circle  would  be  25  feet  x  3*1416, 
and  therefore  this  would  be  the  rate  which  the  rope  would  move  per  revolution 
of  A.  In  60  revolutions  it  would,  therefore,  move  the  rope  60  times  that 
amount,  or — 

25'  X  3-1416  X  60 

The  rope  moving  at  this  rate  about  the  pulley  B,  which  is  5  feet  diameter,  or 
5'  X  3-1416  in  circumference,  then  the  number  of  times  which  the  length  repre- 
senting the  circumference  is  contained  in  the  length  of  rope  passing  over  the 
pulley  in  a  given  time,  will  be  the  rate  at  which  it  revolves.     Therefore — 

25'  X  3-1416  X  60      ,,        ,      .     ,  ,•       ^  t,      onn 

f7 TTzr-rm —  =  the  rate  ot  rotation  oi  13  =  oOO 

5  X  3-1416 

Since,  in  rope  and  belt  gearing,  drums  and  pulleys  always  work  in  pairs — a 
driver  and  driven — and  these  in  calculation  are  always  placed  on  opposite  sides 
of  the  equation — when  one  is  the  numerator,  the  other  is  always  the  denominator. 
The  necessity  for  using  the  constant  3-1416,  to  convert  the  diameter  into  the 
circumference,  occurs  just  as  often  a  numerator  as  a  denominator,  and  it  always 


14  COTTON  SPINNING  CALCULATIONS 

cancel?.      It   is,  therefore,  left  out   of  the   calculation ;    hence  the  rule  is  as 
follows : — 

diameters  of  drivers      revolutions  of  1st  driver  _  ("the  revolutions  of  the  last 
diameters  of  driven  ^  1  "  I     driven  drum  or  pulley 

because— 

diameters  of  drivers  x  revolutions  of  1st  driver     _  ^ 
diameters  of  the  driven  x  revolutions  of  last  driven 

Example  2  (Fig.  4). — Required  the  revolutions  per  minute  of  F,  D,  C,  B,  A 
respectively,  when,  with  the  gearing  as  given  in  Example  1,  G  is  found  to 
revolve  110  times  per  minute. 

Note. — It  is  best  in  working  questions  of  this  kind  to  assume  the  one  moving 
at  a  known  rate  the  driver.  This  always  simplifies  the  calculation,  whether 
dealing  with  rope,  belt,  or  teeth  gear. 

(1)  G  is  a  driver  and  F  driven — 

/,  = —  =  132  revolutions  of  F 

5 

(2)  G,  E,  and  A  are  drivers ;  F,  A,  and  D  are  driven — 

no  X  6  X  12-5  X  25  ^  206-25  revolutions  of  D 
5  X   25    X   8 

(3)  G,  E,  and  A  are  drivers ;  F,  A,  and  C  are  driven— 

110  X  6  X  12-5  X  25       ,„„  •         ,   ,.         ^  ^ 

• — _   =  183-3  revolutions  of  0 

5  X    25    X  9 

(4)  G,  E,  and  A  are  drivers  ;  F,  A,  and  B  are  driven— 

110  X  6  X  12-5  X  25        ooA  ^    I'  e-D 

xxv/_^     /s^  =  330  revolutions  of  B 

5  X    25   X   5 

(5)  G  and  E  are  drivers ;  F  and  A  are  driven— 

110  X  6  X  12-5 


5x   25 


=  G6  revolutions  of  A 


Example  3  (Fig.  4).— What  sizes  of  B,  C,  D,  E,  and  F  would  be  required  in 
order  that  their  revolutions  per  minute  maybe  B,  250;  C,  214;  D,  187  ;  E,  150  ; 
G,  100  respectively,  assuming  A  to  make  GO  revolutions  in  that  time,  and  to 
be  25'  in  diameter  ? 

Here  A  is  the  driver,  and  the  rate  of  the  movement  of  the  ropes  will  be 
GO  X  25'  X  31416  per  minute. 

Since  B  is  required  to  revolve  250  times  per  minute— 

60x25x3-1416 
Circumference  of  B  must  be  = 059 


AND   COSTS   OF   YARN  15 

A-       ,       F-R      9in,'      GO  X  25  X  3-1416 

or  diameter  of  B  x  3-l-il(j  =  — ^.^ 

250 

.    ,.       ,       .„      GO  X  25  X  3-1410      GO  x  25      ., 

/.  diameter  of  B  =  --r^ q^ttt^—  =     o-a      =  ^ 

250  X  3-1410  2o0 

Diameter  of  C  will  be — 

60  X  25  _  „, 
214 

60  X  25      o, 


and  diameter  of  D 


187 


and  diameter  of  E  =  — — ^  =  10' 
loO 


In  case  of  F,  wliich  is  also  a  driver — 
GO  X  25  X  diameter  of  F 


diameter  of  E  x  diameter  of  G 

60  X  25  100 


=  100  revolutions  of  F 


diameter  of  E  x  diameter  of  G      diameter  of  F 

.        60  X  25      _  1 

••  10  X  6  X  100  ~  diameter  of  F 

.A-         ^         ct:^        10  X  100  X  6         ., 

/.  diameter  of  F  -  — ^^ ^ —  =  4 

60  X  2o 

Or,  since  F  and  G  revolve  150  and  100  respectively,  and  G  is  6  feet  in  diameter, 
and  it  is  known  that  their  sizes  must  be  inversely  proportional  to  those  rates, 
then — 

6'  X  100       ,.       ,       „„       ,, 
— ^,_- —  =  diameter  of  F  =  4 
150 

Bale  Breakers  or  Cotton  Pullers. — Fig.  5  is  an  elevation  of  the 
gearing  in  a  well-known  make  of  machine  of  the  Roller  type. 
This  type  of  machine  displaced  manual  pulling,  which  was 
previously  in  vogue,  in  reducing  the  cotton  to  a  suitable 
state  of  mixing.  At  present  this  type  of  machine  is  used 
extensively  in  old  mills  which  do  not  make  a  point  of  keeping 
up-to-date.  In  modern  mills  a  machine  known  as  the  Hopper 
bale  breaker,  or  cotton  puller,  is  found  in  place  of  the  former, 
the  disadvantages  of  the  roller  type  of  this  machine  being  the 
dust  and  noise  accompanied  by  wear  and  tear  and  frequent 
breakages.  Its  forcible  action,  creating  heavy  pressures  upon 
the  cotton  between  edged  surfaces,  are  considered  to  exercise  a 


16 


COTTON  SPINNING  CALCULATIONS 


detrimental  effect  upon  the  cotton.  There  is  a  great  difference 
in  the  principle  of  the  two  types  of  machines  named.  The 
Hopper  has  a  coarse  comhing  action,  and  considerable  pressures 
upon  the  cotton  are  eliminated.     The  productive  capacity  of  a 


Fig.  5. 

roller  pulling  machine  ranges  up  to  100,000  lbs.  per  55i  hours 
when  worked  at  the  highest  pressure.  The  best  results  obtainable 
are  when  it  is  run  at  a  high  speed  for  American  cotton  and  at 
a  moderate  speed  for  Egyptian  and  Indian  varieties. 

The  following  are  the  particulars  of  the  parts  in  the  Eoller 
cotton  puller.  Fig.  5  : — 

a,  the  line  shaft  making  220  revolutions  per  minute. 

h,  a  drum,  19"  in  diameter,  on  the  line  shaft  and  driving  the 
machine  strap. 

c,  c  are  swing  or  *'  gallows  "  pulleys. 

d  represents  the  fast  and  loose  pulleys  on  the  machine  shaft ; 
these  are  16"  diameter. 

e,  a  grooved  rope  pulley,  19"  diameter,  fixed  upon  the 
machine  shaft,  driving  a  rope  which  drives  the  porcupine 
cylinder. 


AND   COSTS   OF   YAEN  17 

/,  a  grooved  carrier  pulley  for  the  above-mentioned  rope. 

g,  a  grooved  pulle}^  lOh"  diameter,  fixed  upon  the  porcupine 
shaft  and  driven  b}'  the  above-mentioned  rope. 

h,  a  wheel  containing  25  teeth,  fixed  on  the  machine 
shaft. 

i,  a  wheel  on  the  shaft  of  the  lower  second  pulling  roller, 
containing  40  teeth,  and  driven  by  h. 

j,  a  wheel  containing  14  teeth,  and  fixed  upon  the  axis  of  i. 

h,  a  wheel  containing  76  teeth,  and  driven  by  j. 

I,  a  wheel  containing  14  teeth,  fixed  to  the  axis  of  k. 

Ill,  a  wheel  on  the  lower  first  pulling  roller,  containing 
76  teeth,  and  driven  by  /. 

n,  a  wheel  fixed  on  the  first  pulling  roller,  containing  17  teeth. 

0,  a  carrier  wheel,  gearing  with  ii  and  j?. 

}),  a  wheel  on  the  lattice  roller  shaft,  containing  20 
teeth. 

q,  a  grooved  rope  pulley,  10"  diameter,  attached  to  e  and 
driving  /•. 

;•,  a  grooved  pulley,  15"  diameter. 

s,  a  wheel  fixed  upon  the  axis  of  r,  containing  20  teeth. 

t,  a  wheel  with  60  teeth,  fixed  on  the  lattice  roller  axis  ti. 

h,  a  wheel  with  60  teeth,  fixed  upon  the  other  vertical  lattice 
shaft  and  engaged  with  t. 

ui  and  ;/3,  wheels  on  lattice  roller  shafts,  each  containing 
38  teeth. 

U2,  a  carrier  wheel,  gearing  with  iii  and  »3. 

u,  a  wheel,  24  teeth,  fixed  to  the  lattice  roller  shaft. 

V,  a  carrier  wheel  engaging  with  u  and  ?f. 

w,  X,  y,  z,  wheels  containing  24  teeth  each,  distributing  lattice 
connections. 

Kevolutions  per  minute  of  the  various  parts  in  the  roller 
cotton  pulling  machine  (Fig.  5). 

The  machine  pulleys r-^  z=  261*25 

mi     r     n  ..•         n      220x19x25x14x14x17     ,„ 
The  feed  lattice  roller i6x40^76x7Xx20  =  ^  ^ 

The  surface  speed  in  inches  per  minute  =  4*7  X  5*5  x  ^^^  =  81"-24 

c 


COTTON   SPINNING   CALCULATIONS 

The  first  pair  of  pulling  rollers — 

■p       ,  ,.  .      ,        220X19X25X14X14       _^ 

iievolutions  per  mmute  =  zrp, — 77;^ — W7> — s^  =  ^'^^3 

^  16x40x76x76 

c     n  ,       220x19x25x14x14x6x22"      ..^„„a 

Surface  speed  =  -^ — ttt — wt^—^^ ^  =113  -76 

^  16x40x76x76  7 

The  second  pair  of  pulling  rollers — 

13      1  r  •     *        220X19X25      _.,  .^ 

devolutions  per  mmute  =  ^^     ,^  =  163'3 

^  16  X  40 

a     f  1  .     ,        220x19x25x6x22  „ 

Surface  speed  per  mmute  = ^^ — ,7^ „  =  3079 

^        ^  lb  X  40  7 


The  porcupine  cylinder 

220  X 

nnt.o   r^ 

16x10 


■D      w  •     ♦        220x19x21        .^„. 

Eevolutions  per  mmute  = 1  a^^mT  ~  522-5 

2 


The  lower  conveyor  lattice  rollers — 

T.      ,   ,.  .      ,         220x19x10x20x60       _  „ _ 

Eevolutions  per  minute  = -^ — - ---  ^^- — „r.  =  o8'05 

^  16x15x60x60 

Surface  rate  per  minute  in  inches  58'05  X  5-5  x  ----  =  1003"'5 

The  right-hand  elevator  lattice  roller — 
220  X 19  X  10  X  20 


16x15x60 


=  58-05 


Surface  rate  =  5805  x  -~^  =  1003"-5 


The  left-hand  elevator  lattice  roller- 

220x19x10x20x60 
16x15x60x60 


=  58-05 


The  first  overhead  conveyor  and  distributing  roller— 
.220x19x10x20x34 


16  X  15  X  60  X  24 


=  58-05 


Surface  rate  =  58-05  X  ^^_iiff  =  1003"'5 


AND   COSTS   OF   YARN  19 

The  second  overhead  conveyor  and  distributing  lattice 
roller — 

220  X  19  X  10  X  20  X  24  X  24  x  24  _ 

10  X  15  X  60  X  24  X  24  x  24  ~  ^'^"^ 

Surface  rate  =  58-05  X  5 '5  X  '^f-  =  1003"-5 

All  the  machines  used  in  connection  with  cotton  spinning 
contain  the  power  to  attenuate  the  cotton.  The  term  which  is 
most  generally  used  in  place  of  the  word  attenuation  is  "  draft." 
The  extent  of  the  ''draft"  governs  the  relative  weight  of  the 
cotton  at  the  different  points  in  the  processes.  The  extent 
practicable  in  each  machine,  and  also  between  the  various  points 
in  each  machine,  should  be  well  understood,  because  it  is  this 
which  governs  the  relation  in  the  weight  of  the  cotton  in  any 
part  of  the  machine. 

If  a  machine,  or  a  part  of  it,  contains  a  draft  of  four,  the 
difference  in  the  state  of  the  cotton,  as  regards  its  weight,  would 
be  four  times.  This  means  that  it  has  become  four  times  lighter 
and  longer  between  the  parts  referred  to. 

The  extent  of  the  draft  may  be  ascertained  from  the  relative 
rates  of  the  parts  moving  the  cotton,  or,  from  the  relation  in  the 
weight  of  the  cotton  as  it  passes  under  the  influence  of  the  two 
points  in  question. 

Applying  this,  in  respect  of  the  machine  under  notice,  it  is 
found  that  the  draft  between  the  feed  lattice  and  the  first  pair  of 
pulling  rollers  is  : 

(surface  movement  of  the] 
first  pair  of  pulling  rollers!     1.4 
..^  .„ pel*  ^i^^^e  1^  i^clies  j 

minute  in  inches  J 

so  that  the  cotton  under  the  influence  of  the  rollers  will  be  1*4 
times  lighter  than  that  upon  the  lattice,  and  therefore  1*4  times 
longer. 

The  following  are  therefore  the  drafts  between  the 
adjacent  parts,  in  progressive  order,  in  the  above-named 
machine : — 


20  COTTON  SPINNING   CALCULATIONS 

First  and  second  pair  of  pulling  rollers — 
3079 


163-3 


=  18-85 


Second  pulling  rollers  and  lower  conveyor  lattices — 

1003-5 

"3079- =  ^^'^ 

Lower  conveyor  and  the  vertical  lattices — 
1003-5 


1003-5 


=  1 


Feed  lattice  and  overhead  conveyor  lattice— 

1003-5  _.._ 
'81-24'  -  ^^  ^^ 

Exercise  1. — What  would  be  the  speeds,  in  revolutions  per  minute,  of  the 
under-mentioned  parts,  if  the  line-shaft  driving  drum  was  16  inches  in  diameter 
instead  of  19  inches  :  (a)  the  machine  pulley ;  (&)  the  feed  lattice  roller ;  (c) 
the  first  pair  of  pulling  rollers ;  {d)  the  second  pair  of  pulling  rollers  ;  (e)  the 
porcupiue  cylinder ;  (/)  the  lower  conveyor  lattice  roller ;  (g)  the  vertical  con- 
veyor lattice  rollers ;  {h)  the  overhead  conveyor  lattice  rollers  ? 

Exercise  2. — What  would  be  the  effect  upon  the  speeds  of  the  different 
parts  if  the  25  wheel  on  the  machine  shaft  was  changed  to  30  after  changing  the 
line-shaft  drum  to  16  inches  ? 

The  working  of  the  first  of  these  exercises  is  as  follows  : — 

220  X  16       ,,,^ 
(a)  — jg—  =  220 

220  X  25  X  14  X  14  X  17      „  ,  ,„ 

^^  40  X  76  X  76  X  20 

,  ,.        4-7  X  16         „„ 

or,  by  proportion  — ^^ —  =  6-'Jb 

, ,  220  X  "25  X  14  X  14       ,  ,^         5-53  x  16         „ . 

(c)  ACS — 7? HR  =  4'66  ;  or t^ =  4-6fa 

^  ^  40  X  76  X  7b  ly 

,,,220x25      ,_.         163-3x61 
i^)   40  ^  '  ^^'         19 "^ 

,.  2-20  X  21        ,,^         522-5  x  16      ,,, 
(^) loi  =  ^^^ '  ''  —IT—  =  ^^^ 

,^,  220  x  10  x  20  X  38       ,.^         58-05  x  16       ,„  „„ 
^^  15  X  60  X  38  =  ^^^ '  ''  -^r—  =  ^^-^^ 


AND  COSTS   OF   YARN 


21 


^,220x10x20       ,_          58-05x10       ,„q„ 
((j) 1-^^-^A  =  ■iS?; ;  or  ^7,; =  48-89 


15  X  60 


19 


.,.  220  X  10  X  20  X  24      ,.,         58-05  x  16      ,_  ^_ 
('0  Tr  ■  ■  ..^       c.  =  48i} ;  or ^^^ =  48-89 


15  X  60  X  24 

Ansioers  to  Exercise  2 — 

(a)  Machine  pulleys,  220. 
{I)  4-759. 
(c)  5-57. 
{d)  165. 


19 


(p)  440. 
(/)  48-89. 
{g)  48-89. 


Fig.  6  is  an  elevation  of  the  gearing  in  a  cotton  pulling 
machine  of  the  Hopper  type.     This  type  of  machine  reduces  the 


Fig.  g. 


cotton  to  a  very  loose  open  condition.  The  advantages  of  this 
machine  over  the  roller  type  of  machine  are — 

Greater  opening  and  cleaning  power. 

Less  noise  and  dust  when  well  constructed. 

Less  personal  attention. 

Greater  production,  about  200,000  lbs.  per  55^  hours,  without 
pressure. 


22  COTTON   SPINNING  CALCULATIONS 

Less  risks  of  fire  in  this  and  subsequent  machines  by  its 
eliminating  hard  substances. 

Mixing  powers  considerable,  whereas  in  the  roller  type  they 
are  very  limited. 

Fewer  breakages  and  up-keep  less  costly. 

The  machine  driving  pulleys  are  on  the  stripping  cylinder 
shaft,  and  in  the  figure  they  are  shown  as  12  inches  in  diameter. 
These  are  driven  by  a  strap  from  a  drum  on  the  line  shaft,  26 
inches  in  diameter,  and  making  220  revolutions  per  minute. 

(1)  Eevolutions  per  minute  of  the  fast  and  loose  drums  of 
the  machine — 

220  X  26 
12 


476| 


(2)  Eevolutions  per  minute  of  the  supply  lattice  roller — 

220  X  26  X   7   X  24  X  24  X  24  ^ 
12  X  20  X  90  X  30  X  30  ~ 

(3)  Eate  per  minute  in  feet — 

29-36  X  5-5  X  22 

T^ ;^  =  42 

12  X   7 

(4)  Eevolutions  per  minute  of  the  spiked  lattice  roller — 

220  X  26  X    7  J<  24  _ 
12  X  20  X  90  ~ 


(5)  Surface  rate  per  minute — 

44-49  X  20  X  22 


=  233' 


12  X   7 

(6)  Eevolutions  per  minute  of  the  regulating  cylinder- 
220  X  26  X   7   X  54 


12  X  20  X  90 
(7)  Surface  rate — 


100-1 


lQQ-1  X  14  X  22  _ 
12  X  T  -  ^^^ 

(8)  Eevolutions  per  minute  of  the  stripping  cylinder — 

220  X  26  , 

12  =  ^^^^ 


AND   COSTS   OF   YARN  23 

(9)  Surface  rate — 

=  1747''5 


476|o<  14  X  22 


12  X   7 

(10)  Revolutions  per  minute  of  the  lower  conveyor  lattice 
roller — 

220  X  26  X   7   X  8 


12  X  18  X  8 

(11)  Surface  rate  — 

185-37  X  5-5  X  22 
12  X  7 


=  185-37 


=  267' 


(12)  Revolutions  per  minute  of  the  elevating  lattice  rollers- 
220  X  26  X   7   X   6 


12  X  18  X  12 


=  92-7 


(13)  Surface  rate- 


92-7  X  5-5  X  22  _        , 
W^f  ~  ^^^  '^ 

Exercise  3. — At  what  rates,  in  revolutions  and  feet  per  minute,  would  each 
of  the  parts  in  Fig.  G  rotate  if  the  driving  puller's  were  altered  to  15  inches 
diameter,  instead  of  12  inches? 

Exercise  4. — Ascertain  the  drafts  between  the  different  lattices  when  the 
conditions  are  as  given  in  Fig.  6,  and  also  when  the  machine  pulleys  are  altered 
to  15  inches  ? 

Exercise  5. — State  the  effects  of  changing  the  24  wheel,  driving  the  90, 
to  20,  upon  the  speed  of  each  part,  when  the  other  conditions  are  as  given  in 
Fig.  6. 

Answers  to  Exercise  3 — 

(1)  381-3  revolutions.  (8)  and  (9)  381-3  and  1398  feet. 

(•2)  and  (3)     235  and    30-G  feet.  (10)  „  (11)  148-3    „    213-62,, 

(4)     „     (5)     35-G    „    18G-4    „  (1-2)  „   (13)     74-1    „    lOG-8    „ 
(G)     „     (7)     80-0    „    300-8    „ 

Ansivei's  to  Exercise  4 — 

When  the  driving  pulleys  are  12  inches  diameter,  the  draft  between  feed  and 
spiked  lattice  is  5-55. 

When  the  driving  pulleys  are  12  inches  diameter,  the  draft  between  spiked 
lattice  and  the  lower  conveyor  lattice  is  1-lG. 


24  COTTON   SPINNING  CALCULATIONS 

"When  the  driving  pulleys  are  12  inches  diameter,  the  draft  between  lower 
conveyor  and  elevating  lattices  is  O'o. 

When  the  driving  pulleys  are  15  inches  diameter,  the  speed  of  all  the  parts 
will  be  decreased  in  the  same  proportion,  and  the  drafts  will  therefore  be 
unaltered. 

Answers  to  Exercise  5  — 

(1)  476^  revolutions.  (8)  and  (9)  Unaltered. 

(2)  and  (3)  24-46         „  ;  35  feet.  (10)     „  (11) 

(4)    „     (5)  37  ,.  194  feet.  (12)     „  (13) 

(6)     „     (7)  83-4  „  313  3  feet. 

The  usefulness  of  this  machine  is  infinitely  greater  than  the 
roller  puller.  Evidence  of  this  is  found  in  the  number  of  mills 
which  have  modified  their  mixing  arrangements  since  its 
introduction. 

The  most  common  practice  in  using  this  machine  is  that  of 
placing  the  cotton  from  the  various  lots  of  bales  in  the  machine, 
in  the  desired  proportions,  at  a  rate  permitting  only  of  the 
limited  exercise  of  their  opening  and  mixing  functions.  When 
such  replaces  stack  mixing,  variations  are  visible  in  all  the 
subsequent  stages. 

Extension  in  the  usefulness  of  the  machine  is  possible  by 
adopting  one  puller  per  30,000  or  40,000  lbs.  per  week,  and 
adjusting  them  so  that  their  maximum  opening  capacities  are 
utilized  in  that  time,  the  cotton,  from  the  several  pullers, 
supplied  with  bale  cotton  in  the  usual  way  but  in  perfect 
rotation,  passing  into  a  common  trunk,  from  which  the  several 
exhaust  openers  draw  their  supplies.  These  latter  deliver  to 
hopper  feeders  attached  to  further  openers,  fitted  with  the  full 
width  type  of  beaters.  From  these  the  cotton  may  pass  to  the 
scutcher  or  to  the  card  direct.  The  hopper  feeder  to  the  final 
opener  should  be  fitted  with  automatic  supply  control  attached 
to  feed  of  the  opener  responsible  for  its  supply.  By  this  system, 
in  a  mill  consuming  200,000  lbs.  of  cotton  per  week,  the  supply 
would  be  drawn  from  six  times  the  usual  number  of  bales,  with 
the  additional  advantages  that  the  hard  and  soft  qualities  would 
be  unavoidably  mixed  in  the  designed  proportions  con- 
tinuously. 

To  derive  the  fullest  benefits  from  the  use  of  the  hopper 

V^^  "     ^_  ''^"  ^^-^  -a-^^  COLL: 


AND   COSTS   OF  YAEN  25 

cotton  puller — as  an  opening  process — it  is  necessary  to  bear  in 
mind  that  the  opening,  and  consequently  the  cleaning  effect,  is 
dependent  upon :  The  rate  of  movement  of  the  spikes  amongst 
the  cotton  and  the  pressure  of  the  cotton  against  the  spiked 
surfaces;  the  distance  of  the  points  of  the  spikes  on  the 
regulating  cylinder  from  those  on  the  spiked  lattice,  and 
the  contrasting  rates  in  the  movement  of  these  two  latter 
parts. 

The  best  speed  of  the  spiked  lattice  is  the  highest  rate  at 
which  it  may  be  worked  without  undue  strain.  The  rate  varies 
considerably  in  the  various  makes,  and  also  with  cotton  treated. 
American  cotton  allows  of  a  higher  rate  than  Indian  or 
Egyptian.  The  most  beneficial  speed  can  be  readily  ascertained 
by  test.  This  decided,  the  regulating  cylinder  should  be  adjusted 
to  a  point  at  which  the  machine  produces  only  the  amount  of 
cotton  required  in  the  fall  working  time.  Where  these  items  are 
disregarded  the  opening  and  cleaning  utility  of  the  machine  is 
only  partially  realized. 


The   Openee. 

Fig.  7  contains  particulars  of  the  principal  parts  and  their 
connections  in  a  hopper-fed  compound  combined  opener.  Par- 
ticulars of  the  other  parts  and  their  connections  are  contained 
in  Figs.  8,  9,  10,  and  11.  The  object  of  giving  the  details  in 
five  instead  of  in  one  figure  is  to  avoid  confusion. 

The  speeds  of  the  various  parts  in  Fig.  7  are — 

Counter  shaft 495       revolutions  per  minute 

Beater  shaft 1028 

Cross  shaft 21417 

Side  shaft 428-34 

Bottom  cone  shaft    .     .     .  856'73  ,, 

Top  cone  shaft     ....  611*95  ,, 

Porcupine  cylinder  .     .     .  440  ,, 

Fan  shaft  (1) 1015-4 

Fan  shaft  (2) 1542 


26 


COTTON   SPINNING  CALCULATIONS 


'220  Revs,  per  min 


Counter 
Shaft    16" 


EXAMILES   OF    WORKING   OUT   THE    SpEEDS    OF   THE    AcOVE   PaKTS. 

^•^O  X  36 

The  counter  shaft  =  — ^,7^ =  490 

lb 


The  beater     ,.     = 

The  cross     „     = 

The  side     ,,     = 

The  bottom  cone  = 

.  The  top    „     = 

The  porcupine  cj'hnder  = 


=  1028 


220  X  36  X  27 
"  16  X  13 


220j^86  ><^27  X   5  _  . 
16  X  13  X  24  ~- 


220 

X  36 

X  27 

X 

5 

X 

30 

103 

16 

X  13 

X 

24 

X 

15 

220 

X  36 

X  27 

X 

5 

X 

30  X 

40 

16 

X  13 

X 

24 

X 

15  X 

20 

220 

x36: 

><27x 

5 

X 

3C 

1x40 

x5 

16  X  13  X  24  X  15  X  20  X  7 
220  X  36  X  18 


=  856-73 

=  61195,  say  612 


16  X  16 

15 


557 


Fan  shaft  (1)  =  557  x  ,;,  =  1285 
Fan  shaft  (2)  =  1028  x  ]}  =  1542 


AND   COSTS   OF   YARN  27 

Exercises  kelatikg  to  Fig.  7. 

(1)  At  what  speeds  would  the  parts  contained  in  this  figure  revolve  if  the 
line  shaft  made  250  instead  of  220  revolutions  per  minute  ? 

(2)  If  the  fan-shaft  pulley  (1)  was  changed  to  G  inches,  at  what  rate  per 
minute  would  it  revolve  ? 

(3)  At  what  rate  per  minute  would  the  bottom  and  top  cones  revolve  if  the 
bottom  cone  and  side-shaft  wheels,  20  and  40,  were  substituted  by  24  and  36 
respectively  ? 

(4)  What  size  of  driving  and  driven  pulleys  would  alter  the  rate  of  the  cross 
shaft  from  214-17  to  257  per  minute?  What  effect  would  such  an  alteration 
have  upon  the  speeds  of  the  other  parts  ? 

(5)  What  changes  would  alter  the  speed  of  the  beater  to  1113  revolutions 
per  minute  if  the  fan  and  cross  shaft  are  to  remain  unaltered? 

(6)  At  what  rates  would  the  top-cone  shaft  revolve  when  the  cone  strap  is 
■working  on  the  extreme  right  and  left  ends  respectively  ? 

Answers  to  Exercises  (Fig.  7) — 

(1)  The  speed  of  all  the  parts  would  be  increased  in  the  same  proportion  as 
the  change  in  speeds,  thus:  502,  11G8,  243-3,  486-7,  973-5,  684,  500,  1153-8, 
1752  respectivelj'. 

(2)  The  surface  rate  of  the  strap  and  pulley  would  be  unaltered,  and  therefore 
the  revolutions  per  minute  would  be  altered  in  same  proportion  as  the  size  of 
pulley,  namely,  to  1100. 

(3)  Bottom  cone,  458-9  ;  top  cone,  645. 

(4)  A  G-inch  driver  on  the  beater  shaft,  or  a  20-inch  driven  on  the  cross 
shaft.  The  side  shaft  and  bottom  and  top  cones  would  be  altered  in  the  ratio 
of  from  5  to  6,  or  to  514,  1028,  and  734  respectively. 

(5)  The  beater  pulley  to  13  inches ;  the  pulley  driving  the  cross-shaft  pulley 
4^*^^  inches,  or  the  cross-shaft  pulley  26  inches ;  the  pulley  on  fan  shaft 
6 J  inches. 

(6)  1562  and  352-7  respectively. 

Calculations  relating  to  the  speeds  of  the  parts  in  Fig.  8. 
Eevolutions  per  minute  of — 

m  1    wr         n  612  X  4  X  9  X  1  X  12      ^  .^^ 

The  supply  lattice  roller  =      9  x  7  x  78^85 —  "    ^^^ 

The  surface  speed  in|  _  0-633  X  55  x  22 
inches  per  minute )  7  ~~ 

The  bottom  lattice  rollers)  ^  612  x  4  x  23  X  17  X  20  x  20  _ 
in  the  hopper  J  9  X  55  x  79  X  48  x  48  ~ 

The  surface  speed  in\  _  4*25  X  5*5  x  22  _ 
inches  per  minute/  7  —*^^ 


28 


COTTON   SPINNING  CALCULATIONS 


The  spiked  lattice  rollersl  ^  612  x  4  x  23  x  17  _  ^^,^„ 
in  the  hopper  /  9  X  55  x  79 


The  surface  speed  in ) 
inches  per  minute/ 


24-47  X  5-5  X  22 


=  422-98 


■g!i« 
f)ui|r{iiiiDiu!iiiliiDiia 


The  regulating  cylinder  = 


440  X    6  X    4  X  24 
12  X  12  X  48 


=  36-6 


AND   COSTS   OF   YARN 


29 


The  surface  speed  in|  _  330 X  18'^ X  22     oQr>.;r  Qi.i72-8ft 
inches  per  minute  J         9  7  ~  ' 

The  stripping  cylinder  = ^^  ~  ^^^ 

The  surface  speed  inl  _ 220 x  16 X  22  _ .. ^ ^^^„  or921-0ft 
inches  per  minute  J  ~  7  "~  ' 

Questions  relating  to  Fig.  8. 
Name  the  parts  affected  by  each  of  the  followiag  alterations,  and  calculate 
the  effects  in  revolutions  and  surface  speed  in  feet  per  minute  : — 

(7)  If  the  cone  strap  was  successively  placed  at  both  extreme  pohits  on  the 
cone  drums. 

(8)  If  the  pulley  on  the  top-cone  shaft  was  5  inches  diameter  instead  of  4. 
('J)  If  the  pulley  on  C  was  changed  to  9  inches  diameter. 

(10)  If  the  80  on  the  supply  lattice  roller  shaft  and  the  12  driving  it  were 
altered  to  84  and  14  respectively. 

Answers  to  questions  rdaiiny  to  Fie/,  8 — 

(7)  When  the  strap  occupies — 

The  lefc-hand 
extreme  position. 

.  14*1  revolutions 

.  244  feet 

.  2 '45  revolutions 

.  42-3  feet 


Spiked  lattice  roller 

>)  jj 

Hopper  lattice  roller 

))  )) 

Supply  lattice  roller 


0'358  revolutions 
6-3  feet 


The  light-hiind 
exLreme  position. 

G2*5  revolutions 
1238  feet 
1084  revolutions 
187-6  feet 
1*615  revolutions 
27-9  feet 


(8)  The  parts  aifected  would  in  this  case  be  the  same  as  in  question  7,  each 
being  increased  in  rate  to  the  extent  of  f ,  or — 

Spiked  lattice  roller 30'58  revolutions 

528-72  feet 


Hopper  lattice  roller 

>>  » 

Supply  lattice  roller 


5"31  revolutions 
91-8  feet 
0-791  revolutions 
13-67  feet 


(9)  In  this  case  only  the  supply  lattice  would  be  affected,  and  this  to  the 
extent  of  Jj  ;  thus — 

Revolutions  of  supply  lattice  roller      ....     0-492 
Surface  speed     .         .  8-5  feet 

(10)  In  this  instance  only  the  supply  lattice  would  be  affected,  and  this  to 
the  extent  of  |2  x  l^,  and  therefore — 

Revolutions  of  supply  lattice  roller  =  0*756 
Surface  speed  =  13-67 


30 


COTTON   SPINNING  CALCULATIONS 


Calculations   relating   to    the   speed   of    the    imrts    found    in 
Fig.  9. 

Eevolutions  per  minute  of — 

m     1  u-         11          612  X   1    X  34  X  27  X  17       „  ^^„ 
The  lattice  roller  = ^r;^- — — — -— ^  =  5*835 


The  surface  speed   of )  ^  5-835  X  3^^  X  22 
the  lattice  in  inches  )  7 


62  X  40  X  33  X  20 
=  55-015 


1  St.  Feedi^olleP 

2nd.  Pressure  i;o*Ter 

2V'y 


612  revs.  J 
per.min  R       C 


—.--.Right  side 

Left  side 

In  aide 


Bottom  Cone   '"^-i  "^20 

Fig.  9. 


The  first  presser  roller  =  612x1x34x27x17x28  ^ 

^  62x40x33x20x35  ' 

The  surface  speed  of  the)  ^  4-667  X  3 '5"  x  22  _ 
first  presser  roller  in  ins. )  7  ~  51'337 

The  lower  feed  roller  =  612^^1   X^x2j 

62  X  40  X  33 


AND   COSTS   OF   YAEN  31 

The  surface  speed  in)       6-865  X  3^'  X  22  ^ 
inches  per  minute )  7 

The  second  presser  roller  = 62  x  40  x  33~x~33  ~  '^'^^ 

The  surface  speed  in)  ^  7-76  x  2|"  X  22  ^ 
inches  per  minute )  7   ~ 

The  pedal  roller  =  ^^'^  ^  L^^  =  8'358 
^  62  X  40 

The  surface  speed  in  I  _  8'4  x  2f "  x  22  _ 
inches  per  minute)  ~  j   —  /ZUi 

Questions  relating  to  Fig.  9. 
(11)  What  would  be  the  effect  of  changing — 

(a)  The  17  on  the  lower  feed  roller  to  16  ? 
(h)  The  27  on  the  pedal  roller  to  32  ? 

(c)  The  cone  strap  to  the  extreme  loft  on  the  cones,  if  their  diameters  at 
those  points  were — bottom,  3J  ;  top,  8^  ? 

Answers  to  questions  relating  to  Fig.  9 — 

(11)  (fl)  The  rate  of  the  lattice  roller  would  be  reduced  to — 

Eevolutions  Surface  speed  in 

per  minute.  feet  per  minute. 

5-592  52-95 

(h)  All  the  parts  dependent  upon  the  27  wheel  for  their  motion  would  be 
aflected  directly  as  the  change,  namely — 


The  lower  feed  roller  to     . 
,,  lattice  roller  to   . 
,,  first  presser  roller  to   . 
,,  lower  feed  roller  to     . 
„  ^second  presser  roller  to 

(c)  Each   of  the   rollers   in   Fig.    9   would   have   their  speed   changed   to 
31        7 
^  X  ^ 3-  X  speed  of  part  when  the  strap  is  in  central  position. 

Calculations  relatiiuj  to  the  speeds  of  the  parts  found  in  Fig.  10, 
the  drivinc)  of  the  heater  being  as  given  in  Fig.  7. 
Eevolutions  and  surface  speed  per  minute  of — 

Topside   )  _220x36x27x  5  x  13x13x24^4455^ 
shaft)  16x13x24x65x38x24      304 


ievolutions 

SuTfice  speed 

er  minute. 

per  minute. 

8-136 

76-68 

6-916 

65-27 

5-531 

60-84 

8-136 

76-68 

9-19 

79-4 

32 


COTTON   SPINNING   CALCULATIONS 


Bottom 
cage 


1- 


220x36x27x  5  Xl3  x  13  X  24  X  24  X  40  X  14  X  44 
16x  13  X  24  X  65  X  38 X  24  x  30  X  28  X  44  x  115 


498960 


=  2-039 

'  =  102"'53 


2128.115 

Surface    ]  _2-039x  16"x  22_ 
speed j  7 

_  220  X  36  X  27  X  5  x  13  x  13  X  24  x  24  x  40  X  14  x  44 

Top  cage  -  16x13x24x65x38x24  x  30  x  28  x  44  x  151 

498960  ,  ...^Q 
=  3^1328  =  ^  ^'^^ 


Too&  Bottom 
Feedroller  to 
the  Beater 
2j"dia, 

Cage  A  / 

Rollers        /;  '"'/"i     "■■ 

3"dia.        //       A/ .,i3"        •,  / 


Bottom 

Calander 

Shaft 


rop 
Shaft 


Fig.  10. 


Surface    1      1-5528  X  21"  x  22 
speed 

Cage 
rollers 


1  = 


=  102"-485 


220x36x27x  5  xl3x  13x24x24x40x14 
16x13 X 24 X  65 X 38 X 24 x 30 X 28 X  20 
178^50^ 
''  1520  ' 


AND   COSTS   OF   TArvN  33 

Surface     1  _  11-72  x  3"  x  22     , ,  ^„  ^ 
speed) ^  =  110  -5 

Bottom      -\  ^  220x36  X  27  X  5  X 13  x  13  x  24  x  24  x  40 
feed  roller]  16  x  13  x  24  x  65  x  38  x  24  x  30  x  28 

_ 35640 

-^28=^^^^ 

Surface     \  _  16*75  x2i"x  22     ,^,„_ 
speed/-"  7  =131  -b 

Exercises  in  Coxxectiox  with  Fig.  10. 
What  would  be  the  effects  if — 

(a)  The  44  wheel  driving  the  bottom  cage  wheel  was  changed  to  4G  ? 

(b)  The  14  wheel  on  the  bottom  feed  roller  was  changed  to  IG? 

(c)  The  24  wheel  on  the  side  shaft  was  changed  to  22  ? 

Ascertain  the  wheels  that  would  make  the  surface  speeds  of  cages,  cage 
rollers,  and  feed  rollers  as  nearly  alike  as  practicable  without  altering  the  rate  of 
the  latter. 

Calculations   relating   to    the   sjjceds   of  the    parts    found    in 
Fig.  11. 

Eevolutions  and  surface  speed  per  minute  of — 

220  X  36  X  27  X  5  x  13  x  13  x  27  X  25  x  33 

16  X 13  X  24  X  65  X  71  X  21  X  25  X  151 

=  2-203 

Q     ,              ,      2-203  X  21"  X  22      .,^n  ,^ 
Surface  speed  = =  =145  '45 

rp,     ,    . ,  220  X  36  X  27  X  5  x  13  x  13  x  27  x  25  x  33 

The  bottom  cage  =  — 


The  top  cage  = 


16  X  13  X  24  X  65  X  71  X  21  X  25  X  115 

=  2-893 

Surface  speed  = s-  =  145"-51 

^,  ,,  220x36x27x  5  x  13x13x27x25 

The  cage  rollers  = -^ — — ^ — ^, — ^j- — =-. — ^ — ^ 

°  16x13x24x65x71x21x16 

=  15-756 

Surface  speed  = —  =  148"-55 

First  or  the   top)  _  220x36x27x  5  x  13x13x27^^.^^ 
calender  [  16x13x24x65x71x23" 

n     ,               .      9-207  X  5"-5  X  22      ,  .^^  i - 
Surface  speed  = ^  =  lo9  -lo 


34 


The  second  calender  = 
Surface  speed  = 


COTTON   SPINNING   CALCULATIONS 

220x36x27x  5  X  13x13x27 


16x13x24x65x71x22 
9-626  X  "5-5  X  22  ^  ^ggr/.g^ 


=  9-626 


The  third  calender  =  ^20x36x27x  5  X  13x  13x27^^p.„3^ 


Surface  speed  = 


16x13x24x65x71x21 
10-084  X  5^^-5  X  22  ^  ^^^..^^ 


23 


The  fourth  or  ,       220  x  36  X  27  X  5  x  18  x  13 


bottom  calender 


;■}  = 


16x13x24x65x71 


=  7-843 


^,     „               ,      7-843  X  7"  X  22      ,^r,>,  ^^ 
Surface  speed  = _-  =  172-55 

mu    1          1,           220x36x27x5x13x21x17     „  ^„^ 
The  lap  rollers  =  -,n .  .-..^..c  ..n^.  .r,.     .^7^  =  7-179 


Surface  speed  = 


16x13x24x65x71x30 
7-179  X  8r  X  22  ^  ^^^,,.^2 


Drafts  in  Openers.— In  the  processes  embraced  in  spinning 
the  cotton  is  attenuated  in  a  somewhat  graduated  manner,  until 


AND   COSTS   OF   YARN  35 

it  is  reduced  to  a  siDScific  weight  per  unit  of  length ;  the  extent 
of  the  attenuation  applied,  in  each  as  well  as  in  the  collective 
processes,  depending  upon  the  ultimate  fineness  or  count  of  the 
yarn  required.  The  attenuation  is  increased  with  the  fineness 
of  the  yarn,  and  it  is  distributed  amongst  the  various  machines 
in  proportions  which  practice  has  proved  most  beneficial.  A 
knowledge  of  the  extent  most  expedient  in  each  process,  as  well 
as  between  the  various  points  in  each  process,  is  therefore 
indispensable. 

"  Draft "  is  the  term  used  to  denote  the  attenuation  or 
difference  taking  place  in  the  unit  of  weight  of  the  cotton  in  the 
various  stages.  It  is  used  also  in  expressing  the  difference  in 
the  rate  of  movement  of  the  parts  of  a  machine.  It  denotes  the 
amount  of  attenuation  occurring  between  two  points,  which  it  is 
customary  to  express  in  terms  of  one  unit  of  the  preceding  of  the 
two  points  specified.  Thus  if  the  draft  in  an  opener  is  said  to 
be  three,  the  rate  of  the  delivery  in  terms  of  one  unit  of  the  feed 
is  three,  and  therefore  the  cotton  is  elongated  to  an  extent  of 
three  times  its  original  length,  and  in  consequence  becomes  at 
least  one-third  of  the  weight  per  unit  of  length  fed. 

The  several  ways  of  proceeding  to  ascertain  the  amount  of 
the  draft  are — 

(a)  By  timing  the  rate  of  movement  of  the  respective 
parts. 

(h)  By  comparing  the  weight  of  the  cotton  per  unit  of  length 
at  the  respective  parts. 

(c)  By  calculating  the  relative  movement  of  the  respective 
parts  by  means  of  the  connecting  gearing. 

The  methods  (a)  and  (h)  are,  of  course,  only  practicable  when 
it  is  convenient  to  work  the  machines.  The  other  method  (c) 
necessitates  particulars  of  the  gearing  only,  and  the  draft  can 
be  ascertained  at  any  time.  It  is  the  method  most  generally 
adopted,  and  is  accurate.  When  it  is  inconvenient  to  obtain 
particulars  of  the  connecting  gear,  an  approximate  result  may 
be  quickly  arrived  at  by  either  of  the  former  methods. 

The  following  calculations  illustrate  the  methods  (a)  and  (c), 
the  speeds  representing  the  former,  however,  being  those  already 
ascertained  by  calculating  from  the  connection  with  the  driving 


36  COTTON   SPINNING  CALCULATIONS 

shaft,  instead  of  by  timing.  Examples  illustrating  the  application 
of  the  method  (b)  will  follow. 

Calculations  rclatinr/  to  the  drafts  hetivcen  the  various  con- 
ti(juous  parts  comprised  in  the  opener,  as  represented  in  Figs. 
7,  8,  9,  10,  ajul  11. 

The  draft  between  — 

The  supply  and  bottom  lattice  (Fig.  8) — 

By  the  calculated!      lS-5"  _n.„-,c, 
surface  speeds  )     10-94" 
or,  by  the  connect-  _  85  x  78  X  7  X  23  X  17  X  20  x  20  x  5.^  =G-714 
ing  gear  J     12x1x9x55x79x48x48x5^, 

The  lower  hopper  lattice  and  the  spiked  lattice — 

By  the  calculated  surface  speeds  =  nroTg^-  =  5  "76 

48  X  48  X  5\ 
or,  by  the  connecting  gear  =  ^q  x"20'x~5^'  "^  ^"^^ 

The  spiked  lattice  and  the  feed  lattice  to  the  porcupine 
cylinder  (Figs.  8  and  9) — 

By  the  calculated]      55*01  _  n.io 
surface  speeds  )  ~  422*98  ~ 

By  the  connect-)     79  X55x9x  1  X  34x27x17x3 
ing  gear  (     17  x23x4x  62x40x33x20x  5>,  ~ 

The  feed  lattice  and  first  presser  roller  to  porcupine  cylinder 
(Fig.  9)- 

By  calculated  surface  speeds  =        „,.   =  0*93 

28  X  3^" 
By  the  connecting  gear  =  ^ ^  =  0*93 

do    X    O 

The    feed    lattice    and   the   first  lower   feed    roller   to   the 

porcupine — 

64'7 
By  calculated  surface  speeds  =  ,_  ^■,  =  1*17 

oo'Ol 

20  X  3 
By  the  connecting  gear  =  -= =  1-17 


AND  COSTS   OF   YARN  37 

The  first  lower  feed  roller  and  the  pedal  roller — 

By  the  calculated  surface  speed  =  ^.      =1-11 

S3  X  2'^ 
By  the  connecting  gear  direct  =  5^^—^  "=  1'12 

Z  (    X    o 

The  pedal  roller  and  the  first  bottom  cage  (Figs.  9  and  10) — 

102'53 
By  the  calculated  surface  speeds  =  rfKj^  =  1"-123 

By  the  connecting  gear  direct 
_40x62x7x20xl5xl3xl3x24x24x40xl4x  44  x  16 
34 X  1  X5x40 X  30 X  65x38x24x30x28x44x151x2^ 
=  1-423 

The  first  bottom  cage  and  the  first  cage  rollers  (Fig.  10)  — 

By  the  calculated  surface  speeds  =  ..  „-,  .^  =  1*078 

15    iu  I'  A'      i.      115  X  44  X  3       69      ,. ^^ 

By  the  connecting  gear  direct  =    , ,   ,,  or>  v    -,a  ~  ri  =  l  08 
•^  °  ^  44   X  20  X  16      64 

The  first  cage  rollers,  and  feed  rollers  to  beater  — 
By  the  calculated  surface  speeds  =  =1*19 

20  X  2' 
By  the  connecting  gear  direct  =  ^  .       o"  =  1"19 

The  feed  rollers  to  beater  and  the  second  bottom  cage  (Figs. 
10  and  11)— 

By  the  calcu- 1  ^  119-78  ^ 
lated  speeds)       131-6 

By  the  connect- 1  _28x30x24x38x27x25  X  25  Xl6^  ^,^^ 
ing  gear  direct  I      40  x  24  x  24  x  71  X  21  x  23  X  115  X  2.^ 

Second  bottom  cage  and  the  second  cage  rollers  (Fig.  11) — 
By  the  calculated  surface  speeds  =  ^  .    ■,..  =  1"02 

By  the  connecting  gear  direct  =  .)o^T('~x~ig  ~  ^^'^ 


38  COTTON   SriNNING  CALCULATIONS 

Drafts  (continued) — 

First  calender  (top)  and  the  second  cage  rollers — 

159'15 
By  the  calculated  surface  speeds  =  i-TnT^r  =  1*07 

By  the  connecting  gear  direct  =  gq  y  oq  y  o'r~  =  1  07 

Second  and  first  calenders — 

By  the  calculated  surface  speeds  =  ^t-q.-ip-  —  I'O-l^ 

23  X  5"'5 
By  the  connecting  gear  direct  =  ooy  K".r.  ~  I'OIS 

Third  and  second  calenders — 

174*30 
By  the  calculated  surface  speeds  =  -r/(p7q-q  =  1'047 

22  X  5"'5 

By  the  connecting  gear  direct  =  ^ ^777^  =  1*047 

As.  X  5  '5 

Fourth  and  third  calenders — 

172*42 

By  the  calculated  surface  speeds  =  frjA^on  =  0*99 

21  X  7" 

By  the  connecting  gear  direct  =  ^ ^777=  =  0*99 

Z I   X  5  '5 

Lap  rollers  and  the  fourth  calender — 

197*42 
By  the  calculated  surface  speeds  =      ^    _  =  1*14 

T>    +r.  r  r      .       71  X  21'  X  17  X  8f       ,  ,  , 

By  the  connecting  gear  direct  =  13  x^rx"30"x  7    ^ 

The  draft  between  the  lap  rollers  and  the  feed  rollers  to  the 
beater — 

By  the  calculated  j.  _  197*42  _ 
surface  speeds    )  ~  TSTG   ~ 

By  the  connecting  )  ^  28  x  30  x  24  x  38  x  21  x  17  X  8  j  _ 
gearing  direct      i       40  x  24  x  24  x  13  x  71 X  30  X  2J  ~ 

By  the  intervening  I  _  J  0*91  X  1-02  X  1*07  X  1*045  X  1*047 
drafts  1  (  -  j       X  0*99  X  1*14  =  1*225 

'  This  dt'ficAency  ix  due  to  the  drafts  between  the  various  parts  being  incompletely 
expressed. 


AND   COSTS   OP  YARN  39 

The  draft  between  the  lap  rollers  and  the  pedal  roller — 

By  the  calculated  I  _  197'42  _  ^-. 
surface  speeds  j       72'01   ~ 

By  the  connect-  _  40  x  62  x  7  X  20  x  15  x  13  x  21  x  17  X  8f  _  ^.^.^ 
ing  gearing  direct  j     34  X  1  X5x40x30x65  x71  X30x2| 

By  the  iuterven- )  _  f  1-423  X  1-078  x  1-19  X  0-91  X 1-02  x  1-07 
ing  drafts  1     j     |      x  1-045  X  1-047  X  0*99  X  1-14-2-30 

The  knowledge  of  the  amount  of  the  draft  between  the  various 
parts  in  a  machine  enables  the  relative  weight  of  the  cotton  at 
each  point  of  its  progress  to  be  ascertained,  provided  any  loss 
between  the  points  in  question  is  allowed  for. 

Thus,  if  in  the  opener  in  question,  the  laps  made  weighed 
at  the  rate  of  12  ozs.  per  yard,  and  the  visible  and  invisible  loss 
therein  amounted  to  3  per  cent.,  and  the  draft  between  the 
various  parts  is  as  calculated  below,  the  weight  per  yard  of  the 
cotton  delivered  by  the  spiked  hopper  lattice  would  be  — 

/Weight  of  1  yard)^  ,  rper  cent,  of  waste\  rthe  draft  between  the 
\     of  opener  lap  /  "^  I     extracted  /       ^     points  in  question 

(a)  (b)         (c)  (d) 

and  .-.  (12-0  ozs.  x  V¥ )  X  2*72  X  1-12  x  1-17  X  0-13 

the  last  four  items  being  the  respective  drafts  from  the  lap 
rollers  to  the  spiked  lattice  :  (a)  that  between  the  lap  and  pedal 
rollers ;  (h)  that  between  pedal  and  the  lower  feed  rollers  to  the 
porcupine ;  (c)  that  between  the  feed  and  lattice  rollers  to  the 
porcupine ;  (d)  that  between  the  feed  and  the  spiked  lattices. 

The  answer  is  5-74  ozs. 

The  weight  per  yard  of  the  cotton  at  the  pedal  roller  would 
be— 

12  ozs.  +  3  per  cent,  lost  on  the  original  weight  X  draft 
or,  12  ozs.  X  Vr  X  2'72 

because  the  cotton  composing  the  lap  has  been  subjected  to  a 
loss  of  as  100  :  97,  therefore  that  must  be  allowed  for  as  well  as 

'   This  deficiency  is  due  to  the  drafts  hetween  the  various  jjarts  being  incompletely 
expressed. 


40  COTTON  SPINNING   CALCULATIONS 

the  length,  contracted  to  the  extent  of  2'72  times  the  length 
delivered,  thereby  increasing  the  weight  to  that  extent.     Thus — 

■^c^     inn     ->  r-o       (  thc  Weight  of  tlic  cotton  1     ^.,  __  , 

12  X  V?  X  2-73  =  {f^^  by  the  pedal  roller  (x) }  =  ^^'^^  ^^'-  P^^'  ^^^ 

The  weight  of  the  cotton  at  any  other  points  may  be  similarly 
calculated,  the  weight  being  only  approximate  if  the  loss  is 
unknown. 

The  following  answers  relate  to  the  weight  of  the  cotton  at 
the  various  points,  the  loss  between  the  pedal  roller  and  first  pair 
of  cages  being  assumed  as  2  per  cent.,  and  1  per  cent,  between 
the  first  and  second  pairs  of  cages.  The  working  of  this  question 
is  given  so  that  the  student  may  accustom  himself  to  the 
working  of  such  exercises. 

The  weight  of  the  cotton  at — 

Feed  lattice  to  porcupine 44"1  ozs. 

Pedal  roller  „  ....      Ans.  =  33'68  „ 

(Working.)  Let  x  =  weight  of  the  cotton  at  the  pedal 
roller — 

— A-rjT   =  weight  of  cotton  at  delivery     .'.  --x-„^--  =  12  ozs. 
.-.  ^  ^^y^"  =  12  ozs.     .-.  «  =  12  X  -Vr  X  2-72  =  33-68  ozs.   Ans. 

First  pair  of  cages A  ns.  =  23*1  ozs. 

Feed  rollers  to  beaters Ans.  =  18*2    ,, 

Second  pair  of  cages .4/is.  =  19'8    ,, 

Between  calenders  3  and  4      .     .     .  Ans.  =  13*68  ,, 

It  is  customary  to  alter  the  draft  by  means  of  the  wheels  on 
the  side  shaft,  also  slight  alterations  by  adjustments  of  the  cone 
strap. 

Exercises  in  Respect  of  Drafts  in  the  Opener  as  per  Details  in  Figs. 
7,  8,  0,  10,  and  11  iNCLUsivF,  WITH  Answers  appended. 

Find  the  drafts  between  the  following  parts  by  gear  direct : — 

(11)  Spiked  lattice  and  pedal  roller.     Ans.  0-171. 

(12)  Spiked  lattice  and  feed  roller  to  the  beater.     Ans.  0-31. 

(13)  Spiked  lattice  and  lap  rollers.     Aiis.  0-212. 


AND   COSTS   OF   YAllN  41 

(14)  Pedal  roller  to  cylinder  and  feed  rollers  to  beater.     Aiis.  1"81. 

(15)  Pedal  roller  to  cylinder  and  second  bottom  cage.     Ans.  2*02. 
(IG)  Pedal  roller  to  cylinder  and  bottom  calender.     Ans.  2"38. 

(17)  Feed  rollers  to  the  beater  and  the  first  calender.     Ans.  1*1. 

(18)  Feed  rollers  to  the  beater  and  the  lap  rollers.     Ans.  1"5. 

(19)  The  second  bottom  cage  and  the  lap  rollers.     Ans.  1"35. 

(20)  First  calender  and  the  bottom  calender.     Ans.  1'08. 

(21)  Assuming  that  this  opener  produced  laps  which  weighed  at  the  rate  of 
13-5  ozs.  per  yard,  what  change  in  that  weight  would  arise  from  each  of  the 
following  alterations  : — 

(a)  Tiie  30  cross-shaft  bevel  changed  to  27  ? 

(b)  The  pinion  on  the  bottom  cone  to  22,  and  that  driving  it  on  the  side 

shaft  to  38  ? 

(c)  The  5-inch  pulley  on  the  beater  shaft  to  6  inches? 

Ans.  12-15  ozs. ;  ll"G6ozs. ;  13-5  ozs. 

(22)  What  changes  would  produce  a  lap  weigliing  10  ozs.  per  yard,  assuming 
that  with  the  gearing  as  in  the  figures  the  lap  made  weighs  12  ozs.  per  yard? 


Scutchers. 

The  Particulars  of  Driving. — Speeds  of  the  parts  in  the 
scutcher  (Fig.  12). 

In  this  figure  B  is  driven  by  a  belt  from  a  25 -inch  pulley  on 
a  counter  shaft,  and  the  latter  is  fitted  with  fast  and  loose 
pulleys,  15  inches  in  diameter,  and  these  latter  are  driven  by  a 
belt  from  a  32-inch  diameter  drum  on  the  line  shaft,  which 
makes  220  revolutions  per  minute. 

The  revolutions  per  minute  of  the  various  parts,  together 
with  the  calculations,  are  as  follows  : — 

Beater  shaft  (B)  =  ^^^  "^  15  x  10  =  ^^^^* 

^  220  X  32  X  25  X  5       „^^  . 

Fan  = -^ =  =  838-1 

15  X  10  X  7 

^  ,     „,       220  X  32  X  25  X    6        „„„  ^ 

Cross  shaft  =  — —r — --  =  586*6 

15  X  10  X  12 

Driver  cone  1  ^  220  x  32  X  25  X   6   X  6.]r 

drum  (D)  (  15  x  10  X  12  x  5|  ~ 

Feed  lattice    ^  220  x  32  x  25  x  6  x  6-5  x  4-5  X  1  X  39  _  ^  . ^o 

roller  (F)  j  15  X  10  X  12  x  5-5  x  4-25  X  88  X  60 ~ 

Surface  rate  = =  51"-121 


42 


COTTON   SPINNING  CALCULATIONS 


AND   COSTS   OF   YARN  43 

p,,      ,,  220x32x25x  6  X6-5X4-5    xl        „,,„ 

Pedal  roller  = — --, — ^-^^ — -- — — — — -^  =  8'342 

15  X  10  X  12  X  5-5  X  4-25  X  88 

Q     ,           ,         8-342  X  2"  X  22       „_„  ._ 
Surface  rate  = „   =  52  -435 

Lap  motion  )  _  220^  32  x  25  x   6   x   8  _  oo ,  p 
shaft  (L)  j  -       "      15  X  10  X  12  x~20  ~  ^"^^'^ 

^  ,,  .^,      220x32x25x6x8x13x20x32     ^  ^^ 

Bottom  cage  (C)  = r-= — :r^ — r?^ — ^rr: — =- — — i — -—  =  3*87 

^    ^  ^  15x10x12x20x71x74x96 

Surface  rate  =  -^-  ^  ^^"  ^  '^^  =  145"-988 

Top  cage  (C)  I      220x32x25x  6x8  xl3x20x  32  _o.,-... 

(19")  )  15x10x12x20x71x74x154" 

c;     ,           ,        2-413  X  19"  X  22       ,,,„.. 
Surface  rate  = -^  =  144-09 

rr,        ,      ,     ,,-,,,      220x32x25x6x8x13x20x19     ,^  ^^^ 
Topcalender(21)  = i5>riOxT2^20-x-7rx  74  x21  =  ^^"^^^ 

Surface  rate  =  ^^'^^^^^"^^^  =  165"-094 


Eevolutions  and  surface  speed  per  minute  of — 

Bottom  calender]  ^  220^x  32  x  25  X  6  X  8  x  13  x  20     , ,  .,  „ 
(19-32)  j  15^00^12X20^71X74"  '^^^' 

Surface  rate  =  ^^^^1'-^^^  =  182-474" 

Lap  rollers  (9.V')  ^  220x32x25  x  6  x  8  x  13  X  11 

diameter)    '  (  15x10x12x20x71x74"   ^^^^^^* 

Surface  rate  =  6:38Ix_9:5:^2  ^  ^^^..^^^ 

Drafts  between — 

Pedal  roller  and  feed  lattice— 

(«)  By  gear  direct  =  |^-^  =  1-025 

"^  ^  39  X  3 

52*435 
{b)  By  the  surface  rates,  already  calculated  =  ^it^tt^  =  1'025 

ol'lzl 


44  COTTON   SPINNING   CALCULATIONS 

Bottom  cage  and  pedal  roller — 

I  A  =  88x4|x5^x  8  Xl3x20x32x  12"  diameter 

^'^        1  X  4.1  X  6.1  X  '20  X  71  X  74  X  96  x  2"  diameter  ~   ^^ 

Top  cage  and  bottom  cage — 

,  .        154x12"      .  _^„ 

^'^^   =  144^09  =  ^^^^ 
Bottom  calender  and  bottom  cage — 

/  ^        96  X  5        ^  ^^^ 
(^^  =  32^ri2  =  1'^^ 

^^^        145-988 --^^^ 
Lap  rollers  and  bottom  calender — 

">    20  X  74  X    5   =  ^'"^ 
,,,  190-696       ,„,^ 

(''^  r82^74  =  1  °^^ 

Lap  rollers  and  bottom  cage — 

^  .     96  X  74  X  11  X  91       ,  ^^^ 

r/A  190-696 

^''^  145^988  =  ^  ^^^ 

Lap  rollers  and  pedal  roller — 

(a)  88  X  4|  X  5^  X  8  X  13  X  11  X  9.1  _  _  __ 
^  ^  ■  1  X  41  X  61  X  20  X  71  X  71  X  2  -  "^  ^"^ 
(h)  190-696 

Lap  rollers  and  lattice  roller — 

60  X  88  X  4j  X  51  X  8  X  13  X  11  X  9i  _  ^  _^ 
^  ^  39  X  1  X  41  X  61  X  20  X  71  X  U>rd  ~  "^'^"^ 
(jb)  190-696  _ 

^'  51-121    "^^^ 


AND   COSTS    OF    YARN  45 


Exercises  ix  respect  of  the  Parts  in  Fig.  12. 

Exercise  1. — What  sizes  of — 

(a)  Beater  pulley  would  be  required  to  give  lOGG  revolutions  of  that  part  per 
minute  ? 

(h)  Counter  shaft  drum  (25  inches)  would  be  required  to  give  12G6  revolu- 
tions of  beater  shaft  per  minute  ? 

(c)  Pulley  on  the  fan  shaft  would  be  necessary  to  give  1173/r  revolutions 
of  fan  per  minute  ? 

(d)  Pulley  on  the  beater  shaft  would  be  necessary  to  drive  the  fan  1675 
revolutions  per  minute  ? 

(e)  To  what  extent  would  the  weight  produced  by  the  machine  be  affected 
by  the  alterations  (a)  and  (b)  respectively  ? 

(/)  What  changes  respectively  in  the  gearing  would  be  expedient  after 
making  the  alterations  (a)  and  (&),  if  it  was  required  that  the  weight  produced 
in  a  given  time  remain  as  before  the  alteration  ? 

Exercise  2. — What  would  the  draft  in  the  machine  (Fig.  12)  become,  if 
the  following  alterations  were  made  in  the  gearing  : — 

(a)  The  8-inch  pulley  on  the  cross  shaft  changed  to  9  inches  and  7  inches 
successively  ? 

(b)  The  65-inch  pulley  on  the  cross  shaft  changed  to  6  inches  and  7  inches 
successively  ? 

(c)  The  65-inch  and  8-inch  pulleys,  both  on  the  cross  shaft,  are  changed  to 
7  inches  each  ? 

Exercise  3 — 

(a)  Ascertain  the  weight,  in  pounds,  per  lap  in  each  of  the  cases  (a),  (h), 
(c).  Exercise  2,  and  also  the  number  of  laps  made  in  10  hours,  assuming  they 
measured  36-7  yards,  and  averaged  22  lbs.  15  ozs.  each,  with  the  gearing 
otherwise  as  per  Fig.  12.     Allow  10  per  cent,  for  lost  time. 

(b)  What  change  in  the  sizes  of  the  6|-inch  or  8-inch  pulleys  on  the  cross 
shaft  would  be  necessary  to  produce  a  lap  12  ozs.  per  yard,  if  that  made  with 
the  gearing,  as  per  Fig.  12,  weighed  10  ozs.  per  yard?  Also,  state  the  differ- 
ence in  the  length  and  weight,  in  both  instances,  which  would  be  caused  by  the 
change. 

(c)  What  effect,  upon  the  output  of  this  machine,  would  result  from  an 
alteration  in  the  position  of  the  strap  on  the  cones  ?  Assuming  the  sum  of  the 
diameters  of  the  cones  at  opposite  points  are  8f  inches,  and  the  strap  is  on  a 
part  of  the  driven  cone  4  inches  in  diameter,  what  would  be  the  weight  per  yard 
of  the  lap  made,  if  that  produced  with  the  gearing,  as  per  Fig.  12,  was  10  ozs. 
per  yard  ? 

(d)  If  the  lap  made  in  a  machine,  geared  as  per  Fig.  12,  averaged  36*7  yards 
and  weighed  22  lbs.  15  ozs.,  and  the  loss  in  the  process  was  2  per  cent.,  and  the 
number  of  laps  used  at  the  feed  4,  what  should*  be  the  weight  per  yard  of  each 
of  the  latter  ? 


46 


COTTON  SPINNING  CALCULATEONS 


AND   COSTS   OF    YARN  47 


Exercises  in  Calculatlno  the  Speeds  and  Duafts  of  the  Various  Parts 
IN  THE  Scutcher  (Fig.  13). 

Calculate  the  revolutions  per  minute  of  the  following  parts.  The  numerals 
signify  the  teeth  contents  in  wheels  and  diameters  of  pulleys  and  other  parts  in 
inches. 

Exercise  4 — ■ 

(a)  Fan  (5  inches).     Ans.  2880. 

lb)  Lap  motion  shaft  (15-30).     Aiis.  400. 

(c)  Side  shaft  (30-60).     Ans.  400. 

(d)  Driver  cone  (4^  inches).     Ans.  800. 

(e)  Driven  cone  (5  inches).     Aiis.  720. 
(/)  Feed  roller  (30-80).     Ans.  9. 

(</)  Feed  lattice  (5^  inches  diameter).     Ans.  4J-Y- 
(^i)  Top  cage  (240)"".    Ans.  4-842. 
(0  Bottom  cage  (190).     Ans.  6-116. 
(/)  Cage  rollers  (20).     Ans.  45-4. 
(k)  First  calender  (23-5  inches).     Ans.  23-15. 
(l)  Second  calender  (22-48-5  inches).     Ans.  24-2. 
(m)  Third  calender  (21-5  inches).     Ans.  25-35. 
(70  Fourth  calender  (29-70-7  inches).     Ans.  18-36. 
(o)  Lap  rollers  (35-120  and  35).     Ans.  14-28. 

Exercise  5. — Calculate  the  drafts  between  the  following  parts  in  the 
scutcher  (Fig.  13) : — 

(a)  Feed  lattice  and  feed  roller.     Ans.  1-0. 

(b)  Feed  roller  and  bottom  cage.     Ans.  4-3. 

(c)  Top  and  bottom  cages.    Ajis.  1-0. 

(d)  Bottom  cage  and  cage  rollers.     Ans.  0-976. 

(e)  Bottom  cage  and  first  calender.     Ans.  1-04. 
(/)  Cage  rollers  and  first  calender.     Ans.  1-067. 
{g)  First  and  second  calenders.     Ans.  1-045. 
(h)  Second  and  third  calenders.     Ans.  1-048. 
(i)  Third  and  fourth  calenders.     Ans.  0-987. 
(/)  First  and  fourth  calenders.     Ajis.  1-11. 

(k)  Fourth  calender  and  lap  rollers.     A^is.  1-0. 
(J)  First  calender  and  lap  rollers.     Ans.  1-11. 
(to)  Feed  lattice  and  lap  rollers.     Ans.  4-763. 

Exercise  6 — 

(a)  Give  the  drafts,  from  4-763  to  3-2,  which  the  following  range  in  sizes  of 
driver  and  driven  draft  change  wheels  would  obtain,  limiting  the  range  in  the 
driver  30-45  with  30  driven,  and  in  the  driven  20-30  with  30  driver. 

(b)  What  single  and  pairs  of  draft  change  wheels,  within  the  following  sizes, 
driver  20-40,  driven  20-50,  will  give  drafts  nearest  4-5,  4-1,  3-8,  3  5,  3-25,  3-0, 
and  2-85  respectively  ? 


48 


COTTON    SPINNING   CALCULATIONS 


Answers  to  Exercise  G  (a)  ■ 


Driver 

31 

32 

33 

34 

35 

36         37 

38 

Draft . 

4-Gl 

4-5G 

4-35 

4-2 

4-08 

3-97       3-8G 

3-7G 

Driver 

39 

40 

41 

42 

43 

44         45 

Draft . 

3-GO 

3-57 

3-48 

3-4 

3-32 

3-24      3-17 

Driven 

30 

29 

28 

27 

2G 

25 

Draft .     . 

4-76 

4-6 

4-45 

4-28 

4-13 

3-97 

Driven 

24 

23 

22 

21 

20 

Draft. 

3-81 

3-67 

3-5 

3-34 

3-17 

Ans^cers 

to  EoL 

ercise  G  (h) — 

4-5   : 

driver 
driven' 

4a-  51 

4  5)    23 

3-25 

=  ff 

4-1  = 

=  u 

3-0 

=  sf;  ft 

3 

8  = 

-24-     2  7 
-30?    35 

;f§ 

3-5 

—  3 e  .    25 

—  48  5     34 

2-85  =  §1 

The  Hunting  Cog  Measuring  or  Length  Motion  used  in  Openers 
and  Scutchers. — In  Fig.  14,  K  and  A  represent  the  calenders  and 


C=^ 


Fig.  14. 


also  the  connecting  wheels ;  H  is  the  drop-shaft  wheel ;  G  the 
drop-shaft  lever,  Gi  being  its  pivot,  g  is  a  projection  of  G  sup- 
ported by  the  lower  part  of  catch  lever  F,  F  is  pivoted  on  P  and 


AND   COSTS   OF    YARN  49 

coupled  to  the  lower  part  of  lever  D  by  Di,  D  having  its  fulcrum 
at  E.  The  spring  I  presses  against  D,  forcing  the  wheel  C, 
which  is  loose  upon  a  stud  attached  to  D,  to  gear  with  wheel  B, 
the  latter  being  fixed  upon  the  shaft  of  the  calender  A.  E  and 
B  are  projections  from  the  sides  of  the  wheels  C  and  B,  which 
are  in  gear.  When  the  projections  meet  the  wheel  C  is  forced 
out  of  gear  with  B,  this  action  causes  the  levers  D,  Di,  and  F 
to  release  g,  and  consequently  G  falls  to  T,  thereby  disengaging 
H  from  J,  and,  since  the  latter  is  driven  by  the  former,  J  ceases 
to  rotate.  The  fall  of  the  lever  G  disengages  the  feed-motion 
clutch  by  rod  connections  with  G  shown  at  point  Z.  The  lap 
continuing  to  rotate  after  the  calenders  have  ceased  delivering 
effects  the  severance  and  completion  of  the  lap. 

The  length  of  the  lap  made  is  governed  by  the  revolutions 
which  the  wheel  B  makes  in  causing  its  projection  to  have 
contact  with  E,  on  C. 

The  revolutions  of  the  wheels  B  and  C,  per  lap,  are  the  least 
whole  numhers  which  express  the  relation  of  their  tooth  contents, 
their  relative  revolutions  being  inverse  to  those  numhers.  Thus, 
if  B  is  21,  and  C  ranged  from  71  to  81  teeth  respectively, 
the  revolutions  of  these  wheels,  per  lap,  would  be  as  given  in 
the  first  part  of  the  table  on  p.  50.  If  B  had  72,  and  C 
ranged  from  71  to  81  teeth,  then  their  revolutions  per  lap  would 
be  as  given  in  the  second  part  of  that  table.  If  C  had  80  and 
B  2  teeth,  then  their  respective  revolutions  would  be  1  and  40. 
Should  C  be  any  number  which  has  no  common  divisor  between 
itself  and  unity,  then,  if  B  contains  less  teeth  than  C,  the 
revolutions  of  B  per  lap  would  be  the  same  as  the  teeth  contents 
of  C. 

Assuming  the  diameter  of  the  calender  5  inches,  then  the 
length  of  the  lap  would  be — 

5"  X  3*1416  X  revolutions  of  B  per  lap  , 
33 i '-^  =  yards 

or,  revolutions  of  B  per  lap  X  0'4363  yard 


50 


COTTON   SPINNING   CALCULATIONS 


Ratio  of  their  teeth 

j 

Sizes  of  the  wheels 

Relative 

rate  of 

contents  expressed 

' 

(in  teeth). 

their  rotation. 

in  smallest  whole 
numbers. 

Revolutions 
of  B  per  lap. 

1 
71 

Length  of  the  lap  in 

yards  as  ascettained 

by  calculation. 

B.     !    c. 

B. 

c. 

B. 

C. 
71 

21            71 

71 

21 

21 

30-98 

21            72 

72 

21 

7 

24 

24 

10-47 

21 

73 

73 

21 

21 

73 

73 

31-85 

21 

.74 

7i 

21 

21 

74 

74 

32-29 

21 

75 

75 

21 

7 

25 

25 

10-91 

21 

76 

76 

21 

21 

76 

76 

33-16 

21 

77 

77 

21 

3 

11 

11 

4-8 

21            78 

78 

21 

7 

26 

26 

11-34 

21      ,      79 

79 

21 

21 

79 

79 

39-47 

21      1      80 

80 

21 

21 

80 

80 

39-90 

21            81 

81 

21 

7 

27 

.7 

11-77 

72            71 

71 

72 

72 

71 

71 

30-98 

72      ,      72 

72 

72 

1 

1 

1 

0-4363 

72      1      73 

73 

72 

72 

73 

73 

31-85 

72 

74 

74 

72 

36 

37 

37 

16-14 

72 

75 

75 

72 

24 

25 

25 

1091 

72 

76 

76 

72 

18 

19 

19 

8-29 

72 

77 

77 

72 

72 

77 

77 

38-59 

72      '      78 

78 

72 

12 

13 

13 

5-67 

72            79 

79 

72 

72 

79 

79 

39-47 

72            80 

80 

72 

9 

10 

10 

4-36 

72            81 

81 

72 

8 

9 

9 

3-96 

Example. — If  C  is  78  and  B  41,  and  the  diameter  of  the  calender  5  inches, 
and  the  draft  between  this  calender  and  the  lap  rollers  1  '045,  then  the  approxi- 
mate length  of  the  lap  ^YOllld  be  as  follows  :— 

The  ratio  of  the  tooth  contents  of  C  and  B  cannot  be  expressed  in  less 
whole  numbers,  and  hence  B  will  make  78  revolutions  per  lap, 

.*.  78  X  5  X  3-141G  x  1-045  =  length  of  lap  in  inches  (approximate) 
=  1280-36  inches  =  106-7  feet 


It  is  found  that,  when  the  lap  is  verj-  thick,  the  lap  exceeds  somewhat  the 
calculated  length  ;  but  as  this  discrepancy^  is  the  same  in  respect  of  each  lap  of 
the  same  weight,  it  is  generally  neglected,  and  the  calculated  length  taken  as  the 
actual. 

The  advantages  of  the  hunting-cog  motion  is  that  it  obtains  the  same  length 
on  each  lap,  and  this  cannot  be  claimed  in  respect  of  the  other  motions.  This 
arises  through  the  slow  and  irregular  disengagement  of  the  knocking-off  catch  in 
the  latter. 

Laps  of  a  length  representing  any  number  of  revolutions  of  the  operating 
calender  can  be  made  by  this  motion. 


AND   COSTS   OF   YARN 


51 


EXEKCISE    7 — 

(a)  How  many  revolutions  would  B  make,  and  what  length  of  lap  would 
result,  if  B  and  C  were  41  and  81  respectively  and  calender  5  inches  diameter  ? 

Ans.  106  feet. 

(b)  What  length  of  lap  would  be  made  if  B  had  42  and  0  81  teeth  when  the 
calender  B  is  5  inches  in  diameter?  Ans.  35-3  feet. 

(o)  What  sizes  of  B  may  be  used  for  a  lap  of  36*2  yards  if  C  had  83  teeth 
when  the  calender  B  is  5  inches  in  diameter  ?  Ans.  1-82. 

Platt's  Knocking-off  Motion 

In  Fig.  15,  K  is  the  bottom  calender  and  A  is  a  single  worm 
secured  to  it ;  B  is  a  worm  wheel  driven  by  A,  and  C  a  pinion 
fixed  upon  the  axis  of  B  ;  C  drives  the 
"knocking-off"  wheel  D,  the  projection 
E  on  D  pulls  the  catch  F  and  the  lever 
G,  to  which  it  is  attached,  in  passing 
that  point.  This  movement  moves  the 
lever  G  to  the  right  on  its  pivot  X  until 
G  ceases  to  support  H.  The  latter  is  the 
drop-shaft  lever  and  in  consequence  of 
the  withdrawal  of  the  support  G,  the  drop- 
shaft  wheel  is  disengaged  from  driving  the 
calenders  and  other  parts  dependent  upon  them  for  their  motion, 
and  hence,  delivery  ceasing,  the  lap  is  completed. 

To  start  a  new  lap,  G  is  raised  at  a  point  on  the  left  to  enable 
the  clearance  of  the  catch  F  from  E,  F  is  supported  by  a 
finger  of  the  right  hand,  whilst  the  left  lifts  the  drop  lever 
H,  when  the  weighted  portion  of  G,  to  the  left  of  X,  causes  it  to 
move  into  a  supporting  position  for  H.  This  action  engages  the 
drop-shaft  wheel,  and  sets  the  delivery  and  feed  parts  in  action. 

The  length  of  the  lap  will  vary  according  to  the  revolutions 
which  the  calender  makes  in  turning  the  wheel  D  one  revolution. 

The  gear  may  be  as  follows : — Bottom  calender,  7  inches 
diameter ;  A,  1 ;  B,  25  ;  C,  18  ;  D,  48. 

The  revolutions  of  A  per  one  of  D  will  therefore  be — 


Fig.  15. 


48    V 
18    -^ 


25 
1 


12  0  0 

IS 


and  the  length  of  the 
lap  in  yards 


1  = 


1200  .7"  X  3-1416 


=  40-724 


18  36 

This  type  of  length  motion  tends  to  the  production  of  laps 


52  COTTON    SPINNING  CALCULATIONS 

slightly  varying  in  length.  This  arises  from  the  slow  move- 
ment of  part  G  during  its  "withdrawal,  and  the  tendency  of  its 
supporting  surface  to  wear  smooth  and  somewhat  rounded  ;  this, 
assisted  by  the  vibration,  causes  the  supporting  part  G  to  fall 
away  at  slightly  varying  intervals 'measured  in  revolutions  of 
the  calender. 

Exercise  8. — Calculate  the  length  of  the  laps — 
(a)  When  C  is  16,  17,  19,  and  20  respectively. 

Ans.  45-75,  43-15,  38-6,  36-15  yards. 

(i)  When  the  following  wheels  are  used  together  instead  of  those  previously 

given:  A,  1 ;  B,  24;  C,  17  ;  D,  50.  A7is.  43-15  yards. 

(c)  When  B  is  altered  to  24?  Ans.  39-1  yards. 

{d)  When  D  is  altered  to  50?  Ans.  42-5  yards. 

Exercise  9 — 

If  a  lap  50  yards  long  is  required,  what  single  wheel  would  give  the  nearest 
result?  Ans.  Changing  D  to  59. 

Exercise  10 — 

If  a  lap  48f  j\irds  was  required,  what  size  of  C  should  be  used  ?    Aiis.  (5). 

Exercise  11 — 

(a)  What  length  of  lap,  in  yards,  would  be  made  if  the  hunting-cog  lap 
length  motion  wheel  on  the  top  calender  contained  82  and  the  wheel  on  the 
knockiug-off  lever  83  teeth  ?  Ans.  40-21. 

(6)  Find  the  time  taken  to  make  a  lap  40-21  yards  in  length, 

Ans.  3  845  minutes. 

(c)  What  would  be  the  weight  of  one  lap  and  also  the  production  in  lbs.  per 
10  hours,  if  2  per  cent,  waste  was  extracted  and  the  time  lost  in  taking  out  the 
laps  and  other  incidental  stoppages  equals  8  per  cent,  and  the  weight  of  the  four 
laps  comprising  the  feed  each  average  11-8  ozs.  per  yard.  Assume  the  length  of 
the  lap  40-21  yards.  Ans.  39  lbs. ;  6006  lbs. 

(d)  What  changes  in  the  gear  would  be  best  to  reduce  the  output  to  a 
normal  amount,  say  to  3000  lbs.  per  10  hours,  v.-ithout  changing  the  count  of 
the  lap  ? 

Ans.  Keduce  size  of  8  inches,  and  increase  size  of  24  inches  in  con-esponding 
proportions  ;  or  8  inches  to  6  inches,  24  inches  to  30  inches. 

Practical  Notes. 

Changes  in  the  Weight  and  Count  of  the  Laps  made  by  Openers 
and  Scutchers. — The  position  of  the  cone  strap  is  automatically 
controlled  by  the  feed  regulator.  To  facilitate  adjustments  in 
the  weight  of  the  lap,  as  circumstances  demand,  an  adjusting 
screw  connection  is  provided.      This  latter,  and  changing  the 


AND   COSTS   OF   YARN  53 

draft  gear,  are  the  means  of  controlling  the  draft,  and  therefore 
of  the  weight  and  count  of  the  lap  made.  The  range  of  adjust- 
ment practicable,  in  respect  of  the  draft  by  gearing,  is  unlimited  ; 
but  that  by  the  adjustment  of  the  cone  strap  is  very  limited,  and 
should  only  be  availed  of  for  temporary  adjustments. 

The  best  position  for  the  cone  strap,  when  the  feed  is  of  the 
mean  or  normal  weight,  is  at  the  centre  of  the  cones.  This  secures 
the  widest  and  most  useful  range  of  action  of  the  cone  strap, 
adaptable  equally  toward  light  and  heavy  variations  in  the  feed. 
When,  by  temporary  adjustments,  so  often  necessitated  by  varia- 
tions in  the  character  of  the  cotton,  and  actions  of  the  machine, 
common  in  ordinary  working,  the  cone  strap  has  been  gradually 
moved  and  settled  in  a  position  otherwise  than  central,  steps 
ought  to  be  taken  to  alter  the  draft  to  an  extent  which  will 
restore  the  cone  strap  to  the  centre  position,  or  otherwise  the 
efficacy  of  this  part  of  the  machine  is  interfered  with. 

The  system  of  connecting  the  feed  and  delivery  parts,  in 
these  machines,  by  belt,  is  being  superseded  by  rope  or  tooth 
gear.  The  method  shown  in  Fig.  12  is  not  always  satisfactory. 
Variations  in  the  slippage  of  the  above-named  straps  affect  the 
draft,  and  add  to  that  arising  from  the  cone  strap.  Positive 
driving  reduces  the  possibilities  of  such  defects  without  intro- 
ducing any  disadvantages. 

Fluctuations  in  the  draft  are  also  often  occasioned  by  variation 
in  the  slippage  of  the  feed  lattice ;  too  highly  tensioned  or  slack 
lattices,  lattice  roller  bearings  out  of  alignment,  and  obstructions 
about  these  parts,  binding  of  the  lattice  against  the  sides,  these 
are  amongst  the  chief  causes  of  variations  in  the  weight  and 
count  of  the  lap.  The  system  of  connecting  the  feed  lattice 
rollers  by  tooth  gear  should  receive  consideration  whenever  the 
variations  in  the  weight  of  the  laps  is  unsatisfactory  and 
cannot  be  eliminated. 

Productions,  Speeds,  and  their  Controlling  Factors. — In  the 
spinning  of  coarse  and  medium  counts  of  yarn  from  American 
and  similar  and  lower  types  of  cotton,  exhaust  openers  are 
extensively  used.  In  these  machines  the  practice  of  dispensing 
the  lap  measuring  and  "  knocking-off"  motion  is  extensive. 
The  advantages  of  such  practice  are,  the  elimination  of  the 


54  COTTON  SPINNING   CALCULATIONS 

thick  and  thin  place,  usually  following  the  stoppage,  and  in- 
creased production ;  it  is  also  a  deterrent  towards  dilatoriness 
on  the  part  of  the  attendant.  Productions  ranging  as  high  as 
40,000  lbs.  per  week  of  55?,  hours  are  not  uncommon  under  such 
conditions. 

The  rate  of  delivery  ranges  up  to  30  feet  per  minute,  and  the 
rate  of  the  feed  about  one-third  of  that  amount.  The  weight  of 
the  cotton  delivered  ranges  to  0*75  oz.  per  yard  per  inch  of 
width,  and  that  of  the  feed  2-5  ozs.  per  yard  per  inch  of  width. 

The  sizes  of  ^feed  rollers  are  from  2j  inches  to  3  inches  in 
diameter. 

The  highest  surface  rates  of  beating  instruments  range  up  to 
10,000  feet  per  minute.  Creighton  porcupines  up  to  1000, 
small  porcupine  cylinders  up  to  1100,  porcupines  (discs)  900, 
large  porcupines  (36  inches  and  upwards)  to  600,  three-bladed 
beaters  to  1250,  two-bladed  beaters  up  to  1500  revolutions  per 
minute. 

Fans  range  up  to  2500  revolutions  per  minute. 

The  Controlling  Factors  in  respect  of  the  Parts  and  Speeds  Named. 
—  Small  feed  rollers  are  only  adapted  for  light  feeds  at  low  rates 
and  pressures.  Feed  rollers  which  have  insufficient  holding 
power  depreciate  the  opening  action  by  allowing  "plucking." 
Overweighting  in  order  to  secure  increased  pressure — better 
holding  power — has  the  same  tendency.  High  rates  of  feed  and 
beating,  as  well  as  heavy  feeds,  require  larger  feed  rollers 
irrespective  of  the  length  of  the  staple.  Too  quick  and  over- 
feeding produces  an  excess  of  good  cotton  with  the  droppings, 
and  interferes  with  the  opening  and  cleaning  actions.  The  sizes 
of  feed  rollers  are  from  2  inches  to  3  inches  diameter  ;  21  inches 
are  only  suitable  when  the  feed  is  light,  slow,  and  the  pressure 
moderate.  High  speeds,  accompanied  by  a  heavy  feed  and 
pressure,  necessitate  rollers  2|  inches  to  3  inches  diameter ;  21 
inches  are  only  adapted  for  moderate  conditions.  Too  close 
setting  of  these  tends  to  weakening  the  fibres,  whilst  the  opposite 
causes  a  stringy  tendency  in  the  appearance  of  the  cotton. 
When  large  rollers  are  used  {^■  inch  would  be  satisfactory  for 
the  heaviest  feed.  With  small  feed  rollers  distances  less  than 
^  inch  are  doubtful, 


AND   COSTS   OF   YARN  55 

High  rates  of  beating  cause  good  cotton  to  be  forced  through 
the  beater  bars,  imparts  a  curly  appearance,  and  also  weakens 
the  fibre. 

Overscutching  is  distinguished  by  the  development  of  the 
curling  tendency. 

There  is  a  great  variation  in  the  rates  at  which  fans  are 
worked.  This  arises  from  constructional  differences  in  respect 
of  the  exhaust  trunks,  passages,  flues,  etc.,  and  dimensions  of 
the  fans.  Deficient  fan  rates  are  signalized  by  the  cotton  being 
overscutched,  desultory  movement  of  the  cotton  from  the  beaters 
to  the  cages,  presence  of  good  cotton  amongst  the  droppings. 
Too  high  rate  of  this  part  is  distinguished  by  the  rapid  flight  of 
the  impurities  along  the  passages,  compact  state  of  the  cotton 
collected  on  the  cages,  absence  of  fine  light  impurities  in  the 
clearing  casements  and  its  presence  in  the  cotton,  low  percentage 
of  impurities  extracted. 

Miscellaneous  Questions  appertaining  to  Opening  and  Scutching. 

(12)  What  number  and  weight  of  laps  would  be  made  in  10  hours  imder  the 
following  conditions  ? — 4  laps  comprise  the  feed  in  the  scutcher,  and  these  average 
10  ozs.  per  yard  each  ;  the  draft  in  the  machine  is  3,  and  the  loss  H  per  cent. 
Tlie  laps  made  are  42  yards  long.  The  lap  rollers  are  9  inches  in  diameter,  and 
make  exactly  9  revolutions  per  minute,  30  seconds  being  lost  at  the  completion 
of  each  lap.  Ans.  108 ;  3720  lbs. 

(13)  How  many  scutchers,  woiking  under  the  conditions  given  in  the  last 
question,  would  be  necessary  to  supply  the  laps  for  108  cards,  assuming  each 
card  produced  120  lbs.  of  0-2  hank  sliver  and  made  5  per  cent,  waste.       Ans.  4. 

(14)  What  should  be  the  length  in  yards,  the  weight  in  pounds,  and  the 
number  of  laps  made  per  10  hours,  if  4  laps,  each  weighing  10  ozs.  per  yard, 
form  the  feed  in  the  scutcher  geared  as  in  Fig.  12,  and  the  time  lost  altogether 
equals  10  per  cent.  ?  Ans.  10-456  ozs. ;  2860  yds. ;  1896  lbs. 

Exercise  15  (Speeds). — Calculate  the  revolutions  per  minute  of  the  principal 
parts  in  Fig.  13. 

Answers — 

Cross  shaft,  400.  Top  cage,  4-84. 

Fan  shaft,  2880.  Cage  rollers,  45-4. 

Side  shaft,  400.  First  calender,  23*15. 

Driver  cone,  800.  Second  calender,  24'2. 

Driven  cone,  720.  Third  calender,  25-35. 

Feed  roller,  9.  Fourth  calender,  18-36. 

Lattice  roller,  4-9,  Lap  rollers,  14-28. 
Bottom  cage,  6-11. 


56  COTTON   SPINNING   CALCULATIONS 

Exercise  16  (Drafts).— Calculate  the  drafts  between  the  following  parts 
in  Fig.  13  : — 

Lattice  and  pedal  rollers.     {Ans.  1.) 

Pedal  roller  and  bottom  cage.     {Ans.  4-3.) 

Bottom  cage  and  cage  rollers.     {Ana.  0"97G.) 
„  „    top  calender.     {Ans.  1-04.) 

First  and  second  calender.     {Ans.  1"045.) 

Second  and  third  calender.     {Ans.  1-048.) 

Third  and  fourth  calender.     {Ans.  0-987.) 

Fourth  calender  and  lap  rollers.     {Ans.  I'O.) 

Production  in  pounds  in  10  hours'  uninterrupted  working,  assuming  the  lap 
weighs  5250  grains  per  yard.     {Ans.  5050.) 

Also,  the  draft  between  the  feed  lattice  and  lap  rollers.     {Ans.  4-76.) 

Also,  tlie  weight,  per  yard,  of  the  cotton  fed,  assuming  the  lap  produced  to 
weigh  at  the  rate  of  5250  grains  per  yard,  allowing  2  per  cent,  for  loss  in  waste. 
{Ans.  25,500  grains.) 


Card  Calculations. 

Fig.  16  represents  the  gearing  common  in  cards  of  the 
revolving  flat  type.  In  the  different  makes  of  these  machines 
wheels  and  other  parts  of  varying  dimensions  are  adopted,  to 
adapt  them  for  the  conditions  under  which  they  work.  The 
subtended  calculations  relate  to  the  speeds  of  all  the  parts  which 
they  contain ;  they  are  arranged  in  the  following  instances, 
as  far  as  convenient,  in  progressive  order.  Slippage  and  thick- 
nesses of  belts  and  ropes  have  not  been  taken  into  consideration 
in  these  calculations,  but  it  is  advisable  to  do  so  in  practice.  In 
belt  drives,  under  bad  conditions,  this  is  sometimes  considerable, 
but  under  fair  conditions  should  not  amount  to  more  than  two 
or  three  per  cent,  at  each  point  in  transmission.  The  actual 
speeds  will  be,  therefore,  somewhat  less  than  the  calculated. 
The  speeds  given  are  those  in  common  use  in  treating  ordinary 
Egyptian  and  the  better  classes  of  American  cotton. 

The  line  shaft  from  which  the  strap  driving  the  card,  in  the 
figure,  is  driven  is  assumed  to  make  220  revolutions  per  minute, 
and  the  drum  upon  it  to  be  12  inches  in  diameter. 

The   dimensions   given  refer  to  the  diameters  in  inches  in 
respect  of  pulleys,  or  teeth  in  cases  of  wheels. 


AND   COSTS   OF    YARN 


57 


58 


COTTON   SPINNING  CALCULATIONS 


Details  of  calculation. 


Lap  roller — 

220xl2xl8x  5  X  28  X  40  x40x  14  Xl7 

15x  7  Xl0xl00x216x40xl20x48 

0-4848  X  6  X  22 

7 

The  feed  roller  (120  x  17  X  21")— 

220xl2xl8x  5  X  28  X  40  x40x  14 

15  X  7iri0  X  100  X  216  X  40  xT2d 

1-369X  2i"x22 


The  lickerin  (7"  X  5")— 


220  X  12  X  18 

15  X  7 

452-57  X  9"  X  22 


The  cylinder  (15"  x  IS"  X  50"  x  GJ")— 
220  X  12  . 
15  " 
176  X  50"  X  22 


The  flats  (40  X  12):  hero,  in  estimating 
the  surface  movement,  it  is  assumed  that  the 
distance  from  centre  to  centre  of  the  flats 
measures  IJ  inches,  and  are  driven  by  a  wheel 
containing  12  teeth,  eacli  of  which  engages  a 
"  flat."  The  worm,  driving  the  worm  wheel 
(40),  has  a  double  tliread. 

220  X  12  X  6^  X   1   X  2   _ 
15  X  12  X  24  X  40 
143   X  12  Xj£'  ^ 
720  X   i   X     1 

Brushes  :  not  shown.  The  driving  gear  for 
the  brushes  that  clean  the  flats  is  not  con- 
tained in  the  figure.  The  speed  of  that  part 
varies ;  under  exceptional  circumstances  it  is 
worked  as  high  as  300  revolutions  per  minute. 
The  normal  rate  of  the  ordinary  brush  is  about 
40  revolutions  per  minute.  A  patent  com- 
bination brush — which  gives  encouraging 
results — is  worked  as  low  as  5  revolutions  per 
minute.  The  stripping  brush  used  in  cleaning 
the  cylinder  and  doffer  is  driven,  during  that 


Revolutions 

per 

minute. 


0-4848 


1-3G9 


452-57 


176 


Surface  speed  per  minute. 


In  inches. 


9-1413 


In  feet. 


0-7GI7 


9-G8 


12786-98 


27657 


143 

720 


0806 


1065-58 


2304-75 


3-574 


AND   COSTS   OF   YAEN 


59 


Details  of  calculation. 


operation,  from  a  groove  in  the  loose  pulley 
on  the  cylinder  shaft,  the  diameter  being 
15  or  10  inches,  whilst  that  on  the  brush 
varies  from  5  to  10  inches,  thus  giving — 


From- 


To- 


220  X  12  X  15 
15  X  10 


220  X  12  X  15  _ 
15x5 

The  doffer  (21G  x  9"  x  40)— 

220  X  12  X  18  X   5   X   28   X   40  _ 
15  X   7   X  10  X  100  X  21G 

176  X  26  X  22  ^ 
15  7 

The  bottom  calender  (30  X  ol)— 
220J<J2J<  18  x5  J<^8_xj0  ^ 
15  X   7   X  10  X  100  X  30 

[Note. — The  dofier  wheel  is  here  a  carrier] 

84-48  X  4  X  22  _ 

7 

The  coiler  delivery  rollers  (10) — 

220xl2xl8x  5  X  28  X40x31x20xl6  _ 
15 X  7  XlOxlOO X 30 X 15 X 20 x  10 

174-57  X  2"  X  22  ^ 
7 

The  coiler  (106)— 
220xl2xl8x  5  X  28  x40x31x20x  38  _ 
15X  7  X10X100X30X15X20X10G 

The  radius  of  the  centre  of  the  coiler  tube 
at  the  point  of  exit  is  3  inches — 

The  distances  traversed  by  this  point      = 

The  can  table  wheel  (82)— 
220xl2x  18  X  5  X  28x  ^OxS  1  x  20  X 16 
15 X  7'x  10 X  100 X 30 X  15 X 20 X 48 

^  16xl4_ 
48x8:i~" 


{ Revolutions 
per 

minute. 


264 


528 


11-73 


84-48 


174-57 


62-5 


Surface  speed  per  minute. 


In  inches. 


In  f(  et. 


0;-)8-78 


r9-898 


1062-03 


88-5 


1097  423 


91-452 


1178  98-16 


5-31 


60 


COTTON   SPINNING  CALCULATIONS 


Details  of  calculation. 


The  number  of  coils  laid  per  revolution  of 
the  cati — 

625 
3-31- 

Occasionally  an  alteration  in  the  rate  of 
the  can  is  necessary  through  considerable 
chantre  in  thickness  of  the  "sliver.  If  the 
8])eed  of  the  can  is  insufficient,  the  adjacent 
coils  adhere  instead  of  freely  uncoiling.  If 
the  rate  of  tlie  delivery  is  greater  than  the 
coiling  rate,  the  sliver  sticks  to  the  sides  of 
the  can.  and  vice  vend. 

The  doflfer  comb  (4")— 

220  X  12  X  18  X  12 

15  X  6  X  I  ~ 

It  is  now  usual  to  furnish  this  part  with  a 
stepped  pulley,  also  the  driver  of  this  is  like- 
wise stepped,  so  that  the  speed  of  the  comb 
may  be  adapted  to  the  rate  of  the  doffer. 

The     grinding    disc,    or    roller,    on    the  ' 
cylinder  (5"  x  7") — 

220  X  12  X  18 


6336  X  7  X  22 

7   ~ 

The  grinding  disc,  or  roller,  on  the  doflfer  • 
the  doflfer  during  grinding  is  driven  from  the 
IS-inch  pulley  on  the  cylinder  during  this 
action,  the  other  gear  being  disconnected, 
the  speed  teing — 

220  X  12  X  18 

15  X  9  =" 
352  X  26  X  22 

7  ~ 

The  direction  of  the  cylinder  when  grind- 
ing is  opposite  to  the  normal  working  direction. 
The  doflfer  rotates  in  the  same  direction.  This 
direction  is  opposite  to  that  indicated  by  the 
bend  of  the  card  wire  in  both  instances. '  The 
direction  of  the  emery  discs,  or  rollers,  is 
opposing  the  movement  of  the  parts  to  be 
ground. 


Revolutions ' 

per 

minute. 


Surface  speed  per  minute. 


18-8 


In  incbes. 


In  feet. 


1581 


15  X  5  ~   I      ^33-6 


13,944 


1162 


352 


28,704 


2392 


An  increased  or  diminished  rate  of  any  of  these  parts  may 
be  obtained  by  altering  the  size  of  any  of  the  wheels  or  pulleys, 


AND   COSTS   OF   YARN  61 

not  a  carrier,  in  the  intercepting  train,  the  effect  being  in  direct 
ratio  in  case  of  drivers,  and  inverse  when  driven  wheels  or 
pulleys. 

The  grinding  of  the  flats  is  done  at  a  similar  speed  to  that 
of  the  cylinder,  rollers  being  preferred  to  discs  for  this  work. 

To  alter  the  Speeds  of  the  Various  Parts. — The  speed  of  the  lap 
rollers  may  be  altered  by  changing  the  48,  driven  wheel,  on  the 
lap-roller  shaft,  and  also  by  the  17,  driver  wheel,  on  the  feed- 
roller  shaft. 

The  speeds  of  the  lap  and  feed  rollers  may  be  altered  by 
changing  the  120,  driven  wheel,  on  the  feed  roller ;  the  14, 
driver  wheel,  on  the  side  shaft ;  the  40,  driven,  on  the  side  shaft  ; 
and  the  40,  driver,  on  the  doffer  shaft. 

The  speeds  of  the  calender,  coiler  delivery  rollers,  coiler  and 
can  wheels  may  be  changed  by  altering  the  doffer,  216,  or  the 
30,  calender  shaft  wheel. 

The  speeds  of  the  doffer,  feed  and  lap  rollers,  calender  and 
coiler  delivery  rollers,  and  also  the  coiler  and  can  wheels,  may  be 
changed  by  altering  the  5-inch  driver  pulley  on  the  lickerin 
shaft,  the  10-inch  barrow  pulley  (driven),  the  28  driver  wheel  on 
the  hub  of  the  latter,  the  100  and  the  40  driven  and  driver 
respectively.  All  these  are  connections  in  the  train  driving  the 
doffer  from  the  lickerin. 

The  speeds  of  all  the  above  parts  may  be  changed  by  any 
alteration  which  increases  the  speed  of  the  lickerin. 

In  the  event  of  a  change  in  the  speed  of  the  lickerin  being 
required  without  change  in  the  speeds  of  the  parts  driven  from 
it,  it  would  be  necessary  to  alter  the  connecting  train  at  some 
point  between  the  lickerin  and  the  doffer  wheel,  inversely  to  the 
former  change. 

Alteration  in  the  movement  of  the  flats  may  be  effected  by 
changing  the  6^ -inch  driver  on  the  cylinder  shaft,  or  the  12- 
inch  driver  pulley  on  the  flat-motion  shaft,  or  the  double,  for  a 
treble,  worm. 


62  COTTON   SPINNING  CALCULATIONS 

Exercises  ke  Alteration  of  Speeds  of  Various  Parts. 

Exercise  1. — If  the  card  cylinder  makes  178  revolutions  per  minute  when 
its  fast  and  loose  pulleys  are  16  inches  in  diameter,  at  what  rate  would  each  of 
its  parts  work  after  changing  the  fast  and  loose  pulleys  to  18  inches  diameter  ? 
Answers — 

Cylinder,  158'2.  Coiler,  50-6. 

Lickerin,  402-2.  Can  wheel,  2-94. 

Doffer,  10-43.  Doffer  comb,  1408. 

Feed  roller,  1-217.  Stripping  brush,  235-470. 

Lap  roller,  0*431.  Grinding  discs,  563. 

Calender,  75-1.  Doffer  (when  grinding),  313. 

Coiler  delivery  rollers,  155-18.  Flats  (inches  per  minute),  1-589. 

Exercise  2. — What  alterations  would  be  necessary  to  restore  the  speeds  of 
all  the  parts  implied  in  the  last  question,  excepting  the  cylinder,  to  the  original 
rates  ? 

Answer's — 

18-inch  pulley  driving  lickerin  to  20-25  inches. 

7-«inch  pulley  driving  barrow  pulley  to  Gfi  inches. 

18-inch  pulley  on  cylinder  driving  the  doffer  comb  to  20.j;  inches,  or  6-inch 

pulley  to  5  j  inches. 
65-inch  pulley  on  the  cylinder  driving  the  flats  to  7-31  inches. 
5-inch  pulley  on  the  grinding  disc  to  4r^  inches. 

Exercise  3. — A  card  having  a  doffer  24-75  inches  diameter,  making  18 
revolutions  per  minute,  produces  550  lbs.  of  sliver  per  week.  The  driving 
pulleys  are  16  inches  diameter,  and  the  cylinder  makes  180  revolutions  per 
minute.  What  size  of  pulleys  would  be  needed  to  reduce  the  speed  to  160 
revolutions  per  minute  ?  What  effect  would  this  change  have  upon  the  revo- 
lutions per  minute  of  the  doffer  as  well  as  upon  the  length  and  weight  produced 
per  week  ? 

A71S.  18  inches ;  ^J-  less  length  ;  488'^  lbs.  per  week. 

The  Drafts  between  the  Various  Parts,  how  ascertained. — The 
draft  may  be  ascertained  by  coraparing  the  weight  per  unit  of 
length  of  the  cotton  at  the  different  points  in  the  machine  ; 
also,  by  timing  the  speeds  of  the  respective  parts  and  ascer- 
taining from  this  their  ratio;  and  again,  by  calculating  the 
mechanical  value  of  the  connecting  train  of  gear  and  dimensions 
of  surface. 

It  is  preferable  wherever  possible  to  do  this  by  the  latter 
system,  as  it  furnishes  the  most  reliable  data.  The  two  other 
ways  serve  very  well  in  ascertaining  approximate  results,  and 
also  in  checking  the  calculated  draft. 


AND  COSTS   OF   YAllN  63 

The  results  given  below  are  arrived  at,  from,  (a)  the 
calculated  speeds,  as  ascertained  in  the  previous  calculations  ; 
(b)  the  connectional  gear  and  sizes  of  the  surface. 

The  drafts  between — 

Lap  and  feed  roller— 

/  N       9-68"        ,  .. 

Feed  roller  and  lickerin— 

(a)  i?^^^^  =  1321 

9-68 

,.     120^x4^x216x100x10x9    _ -,o„-, 
^  ^      14  X  40  X  40  X  28  X  5  X  2 j  ~  "^"^^'^ 

Lickerin  and  cylinder — 


Flats  and  cylinder — 


27657 


(-)  ^;;l  =  15476 

.J      40  X  24  X  12  X  50  X  22'^ 

^  ^     irxT~>r6i  X  llx  12  X  7  ""  ^^^ 


958-78 


Cylinder  and  doffer— 

(«)  ^'-^^  =  0-0346 

V  y  26757       "  ^^^^ 

,j      18X   5   X   28  X  40   X26--  _ 

^  ^      7   X  10  X  100  X  216  X  50"  ~  "  ^"^"^^ 

Doffer  and  calender — 

,  ^       1062-03      ,  ,^„ 

^"^       958-78  =  I-IO^ 


46  COTTON  SPINNING  CALCULATIONS 

Calenders  and  coiler  delivery  rollers — 

,  ,  1097-423      ,  _^.3 

(">  1062^)3   =  1  ^^^ 

31  X  20  X  16  X  2"  _ 
^^^     IS'x  20  X  16  X  4"  -  ^'^^ 


The  Drafts  between  the  Various  Parts,  how  altered. — It  will  be 
seen  from  the  foregoing  that  the  drafts  between  any  of  these 
parts  may  be  altered  by  changing  the  size  of  any  driver,  or 
driven  wheel,  comprised  in  their  connectional  gear.  Increasing 
the  size  of  a  driver  increases  the  rate  of  the  part  nearest  the 
feed,  of  the  two  parts  concerned,  and  therefore  reduces  the  draft, 
and  vice  versa.  Altering  the  driven  wheels  has  the  inverse  of 
the  aforementioned  effects. 

To  ascertain  the  draft  between  other  points  than  those  given 
— which  are  those  contained  in  the  adjacent  parts  progressing 
through  the  machine — all  that  is  necessary  is  to  multiply 
together  the  intervening  drafts  between  the  parts  involved. 
Thus— 

The  total  draft,  i.e.  between  the  lap  and  coiler  delivery 
rollers — 

(a)     =  1-04  X  1332  X  2-16  X  0-0346  X  1-107  X  1-033  =  118-4 

By  comparison  of  the  surface  speeds  of  these  two  parts — 

_  1097-423  _ 
^^^     -^1413^-^^^ 

By  the  connectional  gear  and  sizes  of  parts — 

_  48  X  120  X  40  X  216  X  31  X  20  X  16  X  2"  ^ 
^"^^     ~  17  X    14   X  40  X   30   X  15  X  20  X  16  X  6"  ~ 

The  draft  between  the  feed  roller  and  the  doffer — 
(a)     =  1298  X  2-16  X  0-0346  =  97 

(h)     =^11^^  =  99-04 

_  120  X  40  X  26--  _ 
^'^      -   14   X  40  X  2}   "  ^-^  "^ 


AND   COSTS   OF   YARN  65 

Points  to  be  considered  when  altering  the  Drafts. — The  following 
should  always  be  borne  in  mind  when  deciding  the  drafts  between 
the  various  points  :  — 

The  draft  between  the  lap  and  the  feed  rollers  should  not  be 
more  than  sufficient  to  keep  the  lap  straight.  If  this  is  exceeded 
irregularity  in  the  cotton  fed  will  result.  Smooth  lap  rollers  are 
liable  to  cause  slipping  of  the  lap,  causing  fluctuations,  and 
a  greater  draft  than  that  estimated.  The  corrugated  and  ribbed 
forms  of  lap  roller  eliminate  this  tendency. 

The  draft  between  the  feed  roller  and  lickerin  varies  con- 
siderably. It  is  customary  to  alter  the  speed  of  the  former  part 
whenever  a  change  in  the  draft  is  necessitated.  That  of  the 
latter  part  is  rarely  interfered  with,  being  generally  about  one- 
half  the  rate  of  the  cylinder.  Altering  the  draft  at  this  point, 
therefore,  changes  the  rate  at  which  the  fibres  are  presented  to 
the  action  of  the  lickerin,  and  therefore  controls  the  duration  of 
its  combing  action  upon  any  given  fibre. 

The  draft  between  the  flats  and  the  cylinder  is  regarded 
generally  as  fixed  for  different  classes  of  cotton.  Alterations 
in  this  are  made  by  varying  the  speed  of  the  flats.  The  rate  of 
movement  of  the  flats  in  the  main  governs  the  duration  of  the 
cylinder's  action  upon  a  given  body  of  fibres,  and  also  the 
amount  of  clean  carding  surfaces  introduced,  and  hence  it  is 
proper  to  vary  their  speed  according  to  the  exigencies  of  card- 
ing. With  neppy,  dirty,  and  matted  cottons  a  higher  rate  of 
this  part  is  expedient.  For  low  American,  Indian,  and  like 
qualities  of  cotton,  they  are  worked  at  about  double  the  rate  in 
vogue  for  the  clean  qualities  of  American  and  Egyptian. 

The  draft  between  the  cylinder  and  doffer  is  also  varied, 
probably  more  than  is  expedient.  In  this  the  speed  of  the  doffer 
is  often  regarded  as  subordinate  to  the  count  of  sliver.  The 
propriety  of  this  is  discussed  elsewhere.  The  draft  between  the 
dofler  and  the  calender  is  only  varied  slightly.  It  should  always 
be  such  that  the  sliver,  or  "  web,"  does  not  sag  to  an  extent 
which  is  detrimental.  On  the  other  hand,  if  the  draft  is  too 
much,  irregularity  through  overstretching  will  result.  The 
draft  between  the  calender  and  the  coiler  delivery  rollers  should 
be  sufiicient  to  maintain  a  slight  tension  at  all  times. 

F 


66  COTTOJ^  SriNNING  CALCULATIONS 

Conditions  controlling  the  Output  of  a  Card. — General  con- 
ditions.— When  circumstances  demand  an  alteration  in  the 
quantity  of  the  output,  a  know'ledge  of  the  limitations  of  each 
action  are  essential  in  deciding  the  best  manner  of  procuring 
the  same.  This  knowledge  cannot  be  gained  without  intimate 
association  with  the  work.  Assistance  of  a  general  character 
may  be  afforded,  and  this  is  attempted  in  the  following  state- 
ments. 

Greater  the  contrasting  speeds  of  the  carding  parts,  longer 
the  fibres  are  desired  to  remain  in  the  carding  action ;  greater 
the  length  of  the  fibres  treated,  closer  the  carding  surfaces; 
more  numerous  the  fibres  treated  the  greater  the  tendency  to 
strain  the  fibres. 

The  greater  the  length  of  the  fibres  treated  the  longer  the 
duration  of  the  action  of  carding  by  reason  of  increased  difficulty 
involved  in  their  separation. 

The  more  numerous  the  body  of  fibres  present  in  the  carding 
influences,  beyond  a  certain  limit :  the  greater  the  tendency  of 
damage  to  them  by  rolling  and  excessive  straining.  This  occurs 
whenever  the  quantity  of  fibres  are  in  excess  of  the  capacities  of 
the  available  carding  surfaces,  and  results  in  some  portion  of 
the  weight  of  the  flats  being  borne  by  the  body  of  fibres  instead 
of  by  the  bend.  This  tendency  increases  as  the  crowding  becomes 
more  intense.  This  becomes  apparent  through  the  increased 
power  required  to  drive  the  card.  Such  conditions  are  more 
likely  to  arise  in  treating  long  than  with  short,  fibred  cotton. 
Inconsistent  increases  in  the  power  consumed  by  these 
machines,  after  alterations  of  this  nature,  may  be  regarded  as 
signs  of  overcrowded  carding  surfaces  and  straining  of  the 
fibres. 

Distinct  conditions  in  respect  of  the  actions  of  the  carding  imrts. 
— The  functions  of  the  lickerin  are  to  straighten  the  fibres 
composing  the  fringe  of  the  lap,  eliminate  foreign  matter, 
carry  forward  the  treated  fibres  to  the  range  of  the  cylinder's 
action. 

The  functions  of  the  cylinder  are  to  take  the  fibres  from  the 
lickerin,  to  carry  them  into  the  range  of  action  of  the  card  flats, 
whereupon  the  latter  arrest  those  fibres  otherwise  than  straight. 


AND   COSTS   OF    YARN  67 

The  action  of  the  cylinder,  about  this  latter  portion  of  the 
machine,  is  directly  upon  those  fibres  held  by  the  flats,  and 
partially  projecting  in  the  carding  action.  The  gradual  straight- 
ening and  withdrawal  of  these,  introduces  others  more  or  less 
contiguous  to  the  carding  action.  In  this  way  the  super- 
abundance of  fibres  which  the  flats  receive  during  the  earlier 
period  of  their  action  are  held  in  reserve,  and  gradually 
brought  into  the  action.  As  the  fibres  are  gradually  separated 
and  straightened,  they  are  carried  off  by  the  cylinder. 

The  functions  of  the  flats  are  to  receive  foreign  bodies,  fibres 
that  are  entangled  as  well  as  those  that  are  not  straight — 
not  in  line  with  the  direction  of  the  carding  movement ;  to 
present  such  fibres  to  the  range  of  action  of  the  cylinder  for  a 
definite  period.  The  facility  of  the  flats  to  arrest  and  detain 
foreign  bodies  and  to  retain  and  present  the  fibres  requiring 
carding,  depends  upon  the  efficacy  of  the  points,  composing  those 
surfaces,  and  the  quantity  of  these  available. 

Numerous  sharp  carding  points  accompanied  with  reasonable 
spacing  are  the  active  agents  in  arresting  and  presenting  fibres 
for  disentanglement  and  the  retention  of  foreign  matter  and  short 
fibres.  A  sufficient  supply  of  clean  wire  points  should  be  con- 
tinually passing  into  action.  Should  this  latter  be  insufficient 
the  imperfectly  carded  cotton  from  the  lickerin  would  be  carried 
forward  by  the  action  of  the  cylinder,  and  in  passing  the 
crowded  surface  of  points  of  the  flats,  would  tend  to  embed  those 
fibres  already  engaging  the  wire.  Those  fibres,  brought  forward, 
which  cannot  be  accommodated  byreason  of  the  crowded  character 
of  the  surfaces,  are  subjected  to  the  pressure  previously  referred 
to,  and  are  thus  strained,  ruptured,  and  nepped  according  to  the 
degree  of  overcrowding. 

To  guard  against  the  fibres  becoming  embedded  care  should 
be  observed  to  ensure  that  the  proper  inclination  of  the  bend  in 
wire  is  preserved.  This  is  often  depressed  through  the  stripping 
brush  being  used  in  an  unclean  condition,  also  by  its  being 
set  too  deep.  The  wire  on  all  surfaces  should  have  a  fine 
keen  point,  and  this  should  be  maintained  in  as  uniform  a 
condition  as  possible. 

The  Rate  of  Movement  of  the  Flats.— It  would  seem  that  if  the 


G8  COTTON   SPINNING   CALCULATIONS 

wire  surfaces  act  as  heretofore  described,  a  period  very  much 
less  than  forty  minutes  would  raore  than  suffice  for  the  selection 
of  all  the  desirable  fibres  from  those  received  by  the  fiat  whilst 
occupying  the  first  position  on  the  bend.  Such  may  be  the 
case,  but  since  the  flats  when  even  in  their  last  position  arrest 
fibres— proved  by  passing  a  little  coloured  cotton  in  with  the 
lap,  this  making  its  appearance  on  the  next  flat  exposed — the 
best  way  in  deciding  the  proper  speed  of  flats  is  to  recognize  the 
strips  from  them  as  the  index.  The  speed  should  be  adjusted 
to  give  the  lightest  "strip"  that  will  strip  satisfactorily.  To 
adjust  the  percentage  of  strip  by  manipulating  the  front  stripping 
plate  is  wrong  in  principle.  There  is  only  one  correct  position 
for  that  part,  and  that  is  as  near  the  flats  and  cylinder  as 
practicable.  Increasing  its  distance  from  the  flats  causes  the 
detachment  of  portions  of  the  entangled  fibre  and  impurities 
selected  in  the  carding  action  from  the  flats  as  they  move  out 
of  action,  and  thus  polluting  the  work  otherwise  accom- 
plished. 

In  considering  the  rate  of  movement  of  the  doffer,  its 
functions  as  well  as  the  length  or  the  weight  must  be  kept 
in  mind. 

The  function  of  the  doffer  is  to  take  the  fibres  from  the 
cylinder.  The  more  completely  this  is  accomplished  the  better. 
Should  the  cylinder  be  only  partially  cleared  of  the  fibres 
borne  upon  it,  its  influence  in  carding  will  be  interfered  with 
to  that  extent ;  because  it  reduces  the  extent  of  the  surface  of 
carding  points  at  liberty  to  act  upon  those  fibres  presented  by 
the  lickerin  and  "  flat "  surfaces.  The  aim,  therefore,  in  working 
the  doffer  should  be  to  clear  the  cjdinder  as  completely  as 
possible,  and  to  ensure  this  its  surface  rate  should  be  as  high  as 
practicable.  This  rate  cannot  be  specified  only  in  general  terms 
on  account  of  the  wide  variations  in  the  working  conditions. 
Light  slivers,  poor  staple,  bad  laps,  poor  selvedges,  unsatis- 
factory doffing  combs,  badly  constructed  sliver  casements, 
draughty  rooms,  all  tend  to  restrict  the  speed  at  which  the  doffer 
can  be  run.  Under  favourable  conditions  16  revolutions  per 
minute  can  be  attained. 

The  rate  of  the  flats  is  as  high  as  3  per  minute. 


AND   COSTS   OP   YARN  09 

The  rate  of  cylinders  is  170-180  revolutions  per  minute  for 
low  American  and  like  cottons. 

The  rate  of  cylinders  is  160-175  revolutions  per  minute  for 
Egyptian  and  American  better  qualities. 

The  rate  of  cylinders  is  120-160  revolutions  per  minute  for 
the  longer  stapled  cotton  than  those  enumerated  above. 

Changes  in  the  Total  Draft. — These  are  accomplished  by  altering 
any  of  the  following  four  wheels :  Bevel  wheels  on  the  dofifer 
and  side  shaft  and  feed  roller.  Since  the  side  shaft  transmits 
the  motion  to  the  feed  parts,  a  driver  wheel  will  influence  the 
rate  of  the  feed  in  the  direct  ratio  and  the  draft  inversely,  whilst 
a  driven  wheel  will  have  the  inverse  effect.  It  is  customary  to 
alter  the  draft  by  means  of  the  side  shaft  wheel,  driving  that 
on  the  feed  roller,  and  hence  it  is  called  the  draft  change  wheel. 
Whenever  this  is  impracticable,  on  account  of  the  limits  in  size 
of  wheel  applicable,  it  is  customary  to  alter  that  on  the  feed 
roller  to  an  extent  providing  a  more  convenient  range  of  drafts 
with  the  wheels  available.  Occasionally  the  side  shaft  and  doffer 
bevels  are  altered,  but  usually  these  are  inconveniently  fixed  for 
this  purpose. 

ExKuciSE  4. — What  changes  in  eaoh  of  the  wheels  formhig  the  draft  gear 
in  Fig.  IG  would  give  IGO  of  a  draft,  assuming  the  present  draft  120? 

Workhifj  and  Ansivers^ 

Bevel  wheel  on  doffer  shaft  =  ^^  ^^}-~^  =  30 

Bevel  on  side  shaft  =  —f^f—  =  b^ 

Side-shaft  change  wheel  =  li><J^  ^  jqi  J  (inconvenient ; 

IbO  -  \     too  small) 

Bevel  wheel  on  the  feed  roller  =  ^^^  ^^^''^  =  IGO  i 

Exercise  5.— What  drafts  would  the  following  side-shaft  change  wheel  give, 
respectivel}',  assuming  the  card  contains  120  of  a  draft  when  that  wheel  contains 
18  teeth :  14,  15,  16,  17,  19,  20,  21,  and  22  ? 

Ans.  154-3,  144,  135,  127,  113-6,  108,  102-8,  08-3,  respectively. 

Exercise  6. — What  sizes  of  side-shaft  change  wheels  would  be  required  to 


»  Usually  changed  to  secure  fresh  range  of  drafts  for  the  available  iide-shaft 


chansre  wheel 


70  COTTON   SPINNING   CALCULATIONS 

obtain  the  following  drafts,  assuming    14  gave  a  draft  of  120:    112,  105,  99 
93-5,  88-5? 

Ans.  15,  16,  17,  18,  19. 

Exercise  7. — What  size  of  feed  roller  wheel  would  be  necessary,  assuming 
that  card  drafts  ranging  from  112  to  160  are  required  with  the  side-shaft  change 
wheels  14  to  20  inclusive,  and  a  14  side-shaft  change  wheel  driving  a  120  on  the 
feed  roller  give  120  of  a  draft? 

Ans.  160. 

What  drafts  would  the  various  sizes  of  side-shaft  change  wheels  give  after 
making  the  alteration  referred  to  in  the  last  question  ? 

Anstvers — 
With  the  side-shaft  change  wheel      14         15        16        17         18        19        20 
The  draft  would  be     .        .        .     160     149-3     140     131-8    124-4     118      112 

Weapping. 

For  measuring  sliver  and  roves  a  special  machine  is  used, 
called  a  ■v\'rapping  machine.  This  is  arranged  to  measure  one 
yard  per  revolution.  In  using  this  instrument  care  must  always 
he  taken  to  secure  the  movement  of  the  cotton  in  a  straight 
line  and  also  at  a  uniform  tension,  and  at  the  same  time  pre- 
cautions taken  against  slippage.  Five  or  six  yards  will  be 
sufficient  length,  and  the  sliver  tested  should  be  obtained  from 
different  parts  of  the  can,  and  from  several  of  the  cards  in  the 
"preparation,"  in  order  to  get  precisely  the  conditions  pre- 
vailing. The  cotton,  after  being  measured,  should  be  compactly 
wound  in  the  form  of  a  ball  to  obtain  accurate  weighing. 

Exercise  8. — What  should  be  the  weight  in  grains  per  yard  of  the  sliver 
produced  in  cards  containing  the  following  total  drafts  respectively:  160,  149*3, 
140,  181*8, 124*4,  118, 112,  if  the  loss  in  the  process  m  each  case  amounted  to 
5^  per  cent.,  and  the  lap  fed  weighed  4375  grains  per  yard  ? 
"  Ans.  25-8,  27*6,  29-5,  31*4,  33*2,  35,  36*8  respectively. 

Exercise  9. — AVhat  should  the  sliver  weigh,  per  5  yards,  respectively,  with 
draft  change  wheels  ranging  from  15  to  22  inclusive,  if  5  yards  of  the  sliver 
weigh  134  grains  with  a  14  wheel? 

Ans.  5  dwts.  23^  grs.,  6  dwts.  9  grs.,  6  dwts.  19  grs.,  8  dwts.  4  grs.,  8  dwts. 
14  grs.,  8  dwts.  23  grs.,  9  dwts.  9  grs.,  9  dwts.  18  grs. 

Exercise  10. — What  draft  change  wheel  would  give  slivers  weighing 
9  dwts.  6  grs.,  9  dwts.  20  grs.,  10  dwts.  11  grs.,  11  dwts.  2  grs.,  11  dwts.  17  grs. 
respectively,  per  6  yards,  if  with  a  14  draft  change  6  yards  of  the  sliver  weighs 
203gi-ains? 

Ans.  15,  16,  17,  18,  19. 


AND   COSTS   OF   YARN  71 

The  Names  applied  to  Cotton  in  its  Preparation. 

The  following  are  terms  used  to  designate  the  cotton  in  its 
different  stages  of  preparation  : — 

Yarn  is  the  completely  twisted  thread  of  fihres. 

Eove,  or  roving,  the  band  of  fibres  twisted  to  bind  them 
sufficiently  to  resist  handling.  It  is  thus  described  after  treat- 
ment in  the  slubbing,  intermediate,  roving,  and  "Jack"  machines. 

Sliver,  is  the  band  of  fibres  devoid  of  twist ;  at  least,  it  is 
regarded  as  such.  This  term  is  used  when  the  cotton  is  in  a 
round  state,  in  the  processes,  between  the  carding  and  slubbing 
stages. 

Lap,  denotes  that  the  fibres  are  in  a  sheet  or  ribbon,  formed 
in  a  roll.  This  is  the  state  at  the  opener,  scutcher,  card  sliver 
lap,  ribbon  lap,  and  combing  machines. 

The  System  of  "Counting"  Cotton  in  its  Various  Stages  of  Pre- 
paration.— This  is  adopted  to  express  the  length  per  unit  of 
weight  in  a  concrete  and  simple  form.  The  basis  of  the  system, 
used,  is  that  of  numerating  the  units  of  length  contained  in  one 
pound,  avoirdupois ;  the  unit  of  length,  used,  being  one  hank. 
A  special  length  table  is  used  for  subdivision  of  the  hank.  It  is 
as  follows : — 

54  inches  (1^  yds.)      =  1  thread 
80  threads  (120  yds.)  =  1  lea 
7  leas  (840  yds.)         =  1  hank 

The  table  of  weights  are— 

24  grs.  =  1  dwt. 

18j1t  dwts.  (4371,  grs.)  =  1  oz. 
16  ozs.  (7000  grs.)        =  1  lb. 

Note. — The  work  is  very  much  siraplitied  by  the  adoption  of  grain  weights 
and  pounds.  Much  vahiable  time  is  lost  in  calculation  when  penny- 
weights and  ounces  are  used. 

Thus,  the  count  signifies  the  number  of  hanks,  in  length,  of 
the  cotton  which  are  required  to  weigh  1  lb.,  and  therefore — 

1  hank  (840  yds.)  of  No.  1  =1  lb.  =  7000  grs. 

1  lea  (1  hank,  or  ^f^  yds.  =  120  yds.)  of  No.  1  =  ^"  =  1000  „ 


72  COTTON   SPINNING  CALCULATIONS 

I   lea(T\bank,or^V4''y<^s.=   60yds.)of  No.  1  =  ^^'=   500  grs. 
1  <'-!  540L         =   BO        ")  =rJ^"=   250    .. 

-i-  /    L  84^  =    12  ^  =L'^-=.    100 

10      "     \  70  "  70       "  -^"^     "     /         "  rjQ  ^^^     >i 

J-         <'-J-^  ^-4ft  =      fi          \  =t}^- —      50 

20      "    V140  >'  140      >'  "J     >)     7         5>  240  " 

1_  /    1  8  40  —        1  "I  —        "•—        25. 

120     '>     \840  "  840     >'      ~         -^      5J      ;  ))  ~  840  ~  ''^       " 

The  above  are  the  fractions  of  a  hank  usually  measured 
when  testing  the  count  of  the  cotton  in  the  various  stages  of  its 
preparation. 

In  connection  with  the  weight  table  a  difficulty  is  experienced 
in  remembering  that  IS^^  dwts.  make  1  oz.  To  remember  that 
7000  grs.  make  1  lb.,  and  that  24  grs.  make  1  dwt.,  also  that 
16  ozs.  make  1  lb.,  reduces  the  difficulty  experienced  in  recalling 
the  number  of  pennyweights  per  ounce,  because  the  penny- 
weights may  then  be  reduced  to  grains  and  the  grains  to  pounds. 
If  a  similar  difficulty  occurs  with  the  number  of  grains  in  an 
ounce,  by  noting  that  7000  grs.  are  contained  in  1  lb.  of  16  ozs., 
then  ^f{]o  =  437^,  the  grains  in  an  ounce.  In  this  way  the 
difficulties  so  often  experienced  by  beginners  are  overcome. 

In  order  to  ascertain  the  count  when  the  weight  of  a  given 
length  is  known,  the  procedure  is  to  divide  the  weight  into  that 
of  a  similar  length  of  count  No.  1,  each  expression  being  reduced 
to  common  weight  terms.    Thus — 

Examples — 

For  reasons,  see  page  73. 

(rt)  Required  the  count  when  1  lea  =  50  grains  —  -^t-  =  20 

v'J  })  »  >> ^       "         1  X  24 

(c)  -  437-5        -  -i^-^^~  =  2-285 

(d)      „         „         „    =i]b.     =nr7ooo  =  ^'i^-- 

(e)  „  ,,  1  hank  =  437-5  grains  =  y  =  1^ 


7000 
~    24 

=  292 

7000 
100 

=  70 

1 

~  840  X 

n  "^ 

0-00119 

1  X  ] 

16 

0-01 905 

840  X 

:  1  ~ 

\J   \J X  U\J\J 

1  X  7' 

000 

0-H47 

"840  X 

24" 

•    \J  iJt:  1 

1 

-  840  ^ 

7000 
1 

=  8-3 

AND   COSTS   OF    YAllN 

(/)  Kequired  the  count  when  1  hank  =  24    grains 
(9)  „  „  „        =100         n 

(/*)  „  „  1  yard  =  1  lb. 

(0  „  „  „       =  437-5  grains 

(^)      „         „         „    =1 

Notes  on  the  worhing  of  the  preceding  Examples. 

(a)  The  weiglit  of  1  lea  of  No.  1  =  7-  lb.,  ov^-p-^  grs. ;  thus,  the  numerator 
is  1000  and  the  denominator  50. 

(h)  The  numerator  is  ]  of  the  pennyweights  in  1  lb.,  because  it  is  the  weight 
of  1  lea  of  No.  1  in  pennyweights,  the  weight  expression  of  the  denominator 
used  in  this  case. 

mi  •  1  i.    •     1     i-  1  11  1  X  7000 

The  pennyweights  ui  1  of  1  lb.  -     -  —  ^^ 

These  converted  to  grains  =  M^iu  -  iqoo 
and  1  dwt.  in  grains  =  24 
•    iQoa  —  4.1-7 

(r)  The  numerator  here  is  I  of  1  lb.  in  ounces  =  ^£',  and  the  denominator  1  ; 

.    16  ooQf;  7000  1 

..^^  =2-285...;  or,--  X  437:5 

{(I)  The  numerator  in  this  case  is  again  }  of  1  lb.  and  the  denominator  1 ; 
.-.   }  X  I  =  }  =  0-142... 

(e)  In  this  instance  the  numerator  is  1  lb.,  or  IG  ozs.,  and  the  denominator 

^■^r  lb.  or  1  oz.  respectively,  and  hence  the  count  =  — -  or  ^'-  respectively. 

ic 

(/)  The  weight  of  pounds  and  ounces  can  always  be  more  conveniently 
expressed  in  grains  than  in  pennyweights,  and  hence  the  numerator  is  reduced 
to  7000  grs.,  and  the  denominator  to  24  grs. ; 

•     2.00(1 

(//)  One  over  840  is  the  numerator,  because  it  is  the  weight  of  yard  of 
No.  1  expressed  in  pounds,  and  1  the  denominator. 

Exercise  11. — What  are  the  counts  of— 
(a)  1  lea  =  4  dwts.  4  grs.  ? 
(&)  60  yards  =  2  dwts.  2  grs.  ? 


74  COTTON    SPINNING  CALCULATIONS 

(c)  95  yards  =  50  grs.  ? 

(d)  21  leas  =  125  grs.? 

(e)  4  leas  =  1  dwt.  16  grs.? 
(/)  1  yard  =  1  dwt.  1  gr.  ? 
(g)  5  yards  =  7  dwts.  12  grs.  ? 
(h)  1  yard  =  12  dwts.  ? 

What  should  be  the  weight  in  grains  of — 

(i)  1  yard  of  No.  1  ? 

(j)  1  lea  of  40',  3G\  84^  79'  ? 

(k)  30  yards  of  4'  ? 

(0  60  yards  of  10'? 

(m)  6  yards  of  0-2'  ? 

(n)  15  yards  of  0-25'? 

(o)  1  yard,  0-0340,  in  ounces? 

Exercise  12. — What  would  be  the  count  and  weight  in  ounces  per  yard  of 
the  laps  fed  in  cards  containing  each  120  of  a  draft  if  the  amount  lost  in  waste 
is  5  per  cent.,  and  the  count  and  weight  of  the  sliver  are — 

Kespective  count 

Kespective  weight  in  grains  per  yard 

Ans.  Count  =  0-002225 
Ounces  per  yard  =        9 

Exercise  13. — What  would  be  the  count  of  the  sliver  and  its  weight  in  grains 
per  yard  if  the  draft  in  the  card  was  152  and  the  lap  weighed  80  ozs.  per  yard, 
the  loss  in  waste  being  5  per  cent.  ? 

Ans.  Count  =:  0-32 

Weight  =  27-35  grs. 

Exercise  14. — What  weight  of  sliver,  in  grains  per  yard  respectively,  would 
be  necessary  to  enable  a  card  to  produce  800  lbs.  of  sliver  per  week  of  55 
working  hours  with  a  doffer  126£  inches  diameter  when  run  at  16,  15,  14,  13, 
and  12  revolutions  per  minute  respectively? 

Ans.  45-5,  48-5,  52,  56,  61-7. 

Exercise  15. — What  would  be  the  count  and  weight  of  the  sliver,  in  grains 
per  yard,  in  cards  containing  120  of  a  draft,  if  the  lap  fed  averaged  10,  11,  12 
13,  and  14  ozs.  per  yard  respectively,  and  the  waste  in  carding  was  5^  per  cent.  ? 

Ans.  0-242  0-22  0-202        0-86  count. 

34-4  37-85        41-3  44-75  weight  in  grains  per  yard. 

Exercise  16. — What  should  be  the  weight  of  the  sliver,  in  grains  per  yard, 
produced  by  a  card  containing  120  of  a  draft,  if  the  lap  weighs  10  ozs.  per  yard 
and  the  waste  extracted  is  5  per  cent.  ? 

Ans.  34-6  grs. 


0-267 

0-241 

0-192    0.16 

d  312 

34-6 

43-3    52 

0-002083 

0-0016 

0-00133 

10 

12,^ 

15 

AND   COSTS   OF   YARN  75 

Exercise  17. — What  should  be  the  weight  of  the  lap  suitable  for  a  card  it 
the  loss  in  waste  is  5  per  cent.,  the  draft  being  120  and  the  sliver  is  required 
to  weigh  36  grs.  per  yard  ? 

Ans.  4547  grs.,  or  10-38  ozs. 

Exercise  18. — At  what  rate,  in  revolutions  per  minute,  should  the  doffer  in 
a  card  be  worked  in  order  to  produce  400  lbs.  of  sliver  of  34*G  grs.  per  yard 
in  54  liours'  continuous  working,  if  the  doiler  is  24*75  inches  in  diameter  and  the 
draft  between  this  part  and  the  coiler  delivery  roller  is  1*10  ? 

Ans.  10"5  revolutions. 

The  Length  of  Fillit  required  to  Cloth  the  Cylindrical  Surfaces. — 
In  calculating  the  length  of  the  fillit  required,  it  is  necessary 
to  allow  one  coil  extra  in  addition  to  that  sufficient  for  holding. 
Thus,  a  cylinder  50  inches  diameter,  38  inches  wide,  to  be 
covered  with  fillit  2  inches  in  width,  would  require  4f  coils  +  1, 
and  the  length  for  holding,  say,  about  6  feet — 

/.  f  ^  X  -2^-  X  ^-  feet  +  6  feet  =  268  feet 

Doffers  24  inches  diameter,  38  inches  wide,  clothed  with  1^  inches 
fillit,  require  about  4  feet  for  holding,  and — 

fl  X  ^^  X  -^^  feet  +  4  feet  =  130  feet 

The  following  is  the  procedure  in  forming  the  spirals,  termed 
"  half-lap "  and  tapered  tail  ends,  respectively.  The  latter  is 
commenced  the  width  of  one  staple  and  increased  gradually  to 
the  full  width  in  a  length  equal  to  the  first  coil.  The  former  is 
commenced  one-third  or  one-half  the  width,  and  the  spiral 
obtained  in  one  and  a  half  or  two  coils,  the  finishing  ends 
terminating  in  the  inverse  manner. 

Example  of  preparing  "Half-lap." — Assuming  the  fillifc  contains 
six  columns  in  the  width,  half  the  width  will  be  convenient  for 
the  commencement;  maintain  this  width  for  half  a  coil,  and 
then  proceed  to  add  a  column,  on  the  right-hand  side,  at  points 
equidistant  in  the  next  half  coil.  In  doing  this  it  is  necessary 
to  have  the  commencement  of  the  last  row  of  each  column  a 
distance  from  the  first  row  of  the  next  column  of  ^  of  A  of  l  the 
circumference  of  the  cylinder.  Thus  three  columns  would  be 
added  in  the  latter  half  of  the  first  coil.  Afterwards,  com- 
mencement is  on  the  right  hand,  the  left  half  of  the  end  of  the 
first  coil  must  be  secured  to  the  "jump-end"  of  the  beginning 


76  COTTON  SriNNTNG  CALCULATIONS 

of  the  first  coil,  and  the  second  coil  is  commenced  with  the 
right-hand  half.  The  left-hand  portion  is  prepared  for  the  cut- 
away portion  as  follows  :  Proceed  to  widen  the  right  half  of  the 
second  coil  by  the  addition  of  rows  and  columns  on  the  left-hand 
side  in  the  same  manner  and  at  the  same  rate  as  with  the 
tapered  portion  of  the  first  coil,  but  from  the  commencement  of 
the  second  coil,  thereby  obtaining  the  full  width  at  a  point 
opposite  the  commencement  of  the  taper  in  the  first  coil.  This 
completes  the  preparation  for  cutting. 

When  the  columns  are  odd  in  number,  for  instance,  seven, 
commence  with  the  width  of  three  columns  to  extend  over  2  of 
the  circumference,  and  then  proceed  to  make  the  tapered  portion 
over  the  remaining  i  of  the  first  coil,  and  put  in  the  remaining 
three  columns  required  to  complete  the  spiral,  in  the  first  2  of 
the  second  coil.  In  the  former  instance  the  spiral  extends  over 
1^,  coils  at  each  end,  and  in  the  latter  over  If. 

The  tapered  tail  end — completed  in  one  coil — is  defective  in 
that  the  terminals  cannot  be  sufiiciently  tensioned  for  satis- 
factory grinding  and  working.  The  tapering  should  always  be 
on  the  inside  and  not  on  the  outside,  this  being  the  most  com- 
mon method.  Extending  the  taper  in  half-lap  over  the  whole  of 
the  first  coil,  necessarily  extends  the  taper  over  the  second  coil. 
This  would  largely  reduce  the  number  of  wire  points  over  these 
portions,  making  wide  gaps  of  absent  points.  The  finishing-oft" 
preparation  is  exactly  the  inverse  of  the  commencement. 

licmemher  that  uniformity  in  the  character  of  the  point 
is  dependent  upon  uniform  resilence  of  the  wire,  and  this 
support  it  obtains  through  the  medium  of  the  tension  at  the 
foundation. 

The  Slivee  Lap  ^Machine. 

Fig.  17  represents  some  of  the  principal  parts  and  the 
gearing  in  the  sliver  lap  machine. 

The  object  of  this  machine  is  to  prepare  a  ribbon  of  fibres  of 
uniform  width,  weight,  and,  as  far  as  practicable,  with  the 
fibres  laid  parallel  and  distributed  uniformly.  This  latter  is 
only  partially  obtained,  and  hence  the  succeeding  process. 


AND   COSTS   OF   YARN 


11 


The    machine    consists     of    parts    having     the    following 
functions : — 


29 


72 


50 


26 
33 


6*1 


64- 


12"Dia. 


12'Dia. 


5  Dia. 


5  Dia. 


l2Dia. 


1^Dia. 


30 


30 


73 


21 


21 


16  Dia. 


I^Dia.  - 

22, 


26 


Fig.  17. 


(a)  The  feed  parts,  not  shown,  for  presenting  a  fixed  number 
of  the  carded  sHvers  in  uniform  tension,  alignment,  and  placed  as 


78  COTTON   SPINNING  CALCULATIONS 

close  as  practicable.  Also  means  for  the  detection  of  missing 
slivers  and  stopping  the  machine. 

(&)  The  rollers  (1[,  X  li  X  ll)  for  attenuating  the  above- 
named  slivers  to  the  most  beneficial  extent,  this  is  generally  up 
to  about  2. 

(c)  The  calenders  (5"  X  5")  for  smoothing  and  pressing  the 
attenuated  ribbon  of  fibres. 

(cl)  The  lap  rollers  (12"  x  12")  for  winding  the  continuous 
ribbon  of  fibres  tightly  upon  a  wood  roller. 

Calculations  relating  to  the  Sliver  Lap  Machine  (Pig.  17). — This 
machine  is  driven  by  a  strap  from  a  9-inch  drum  on  a  line  shaft 
making  220  revolutions  per  minute. 

The  calculated  revolutions  per  minute  of  the  various  parts 
are  as  follows  : — 

Machine     shaft ,_  ^^^^  ^-         220x9 
(16"-13-29)         /  -  ^"^"^  ^^>  °^''  ~~16~ 

First  drawing  roller  \  _  o  ,  o         220  X  9  X  29  X  21  x  50  X  41  X  33 

(64-26-U")  I  -  «^  -,  or,  16  x  72  X  21  X  26  X  24  x"64 

Second     drawing  \  _  qq  f;         220  X  9  X  21  x_50  X  41  x  33  X  26 

roller  (22-1^"    /  "  '^'^'^>  ^^''  16  x  21  x  26  X  24  x  64  X  22 

84-2x26 
or,  — 22— 

Third  drawing  roller^  _.noo         220  x  9  X  29x21x50  X  41 
(24-33-U")  /  -  ^^^  ^'  0^'  16  X  72  X  21  X  26  X  24 

First    and    second]  220x9x29 

calenders  >  =  49'8,  or, --. — z^ 

(50-5"),  (72-5")       J  1^  ^  7^ 

,  220  X  9  X  29  X  21 
^""^  16^02^^ 

Lap      rollers           .       „^  ^ ,          220  x  9  x  13 
(12"-73-30)  }  =  22  04,  or,  ^^^^ 

220  X  9  X  13x30 
16x73x30 
Drafts — 

Between  second  and  \      -, .-,  o      .   26  x  11" 
first  rollers  /  -  1  1°,  or,  22x1.^" 

Between  third   and  \  _  ^  22  x  64  X  1^ " 

second  rollers        /  —  1  "4,  or,  26x33x1}" 


and 


AND   COSTS   OF   YAEN  79 

Between  third  and^  _  -,  q  <         64x1?/ 
first  rollers  /  -  l'-^^,  or,  ^^  ^  ^y, 

Between    calender  \  _  -,  ^-,  .         24  X  26  x  5" 

and  third  roller    /  "  ^'^^^^  °^''  41  X  50  x  V/ 
Between    calender  |  _-,.n7      .   64  X  24  x  26  X  5'' 

and  first  roller     /  -  ^"^ ' '  ^^''  33x 41  x 50 X  IV' 
Between  lap  roller!  72x13x12^^ 

and  calender        •'  ~         '  °^''  29  X  73  x  5" 

Between   lap  roller  ^  _  64  x  24  x  26  X  21  X  72  x  13  X  12" 

and  first  roller      }  "  '^'^^'  °^'  33  x  41  x  50  x  21  x  29  X  73  X  1  y' 

Production. — What  should  the  lap  weigh  in  grains  per  yard 
if  the  number  of  slivers  fed  are  14,  and  each  weigh  30  grains 
per  yard  ? 

,        ,_^  14  X  30 

Ans.  202,  or,  -^^^^  . 

What  should  be  the  weight  of  lap  produced  in  pounds  per 

week  of  55  hours,  no  allowances  ? 

^,^^         2204  X  55  X  60  X  12  X  22  x   202 
Ans.  2182,  or, ^^^  7    X  700~0- 

What  length  in  hanks  per  week  should  be  delivered  under  the 
conditions  given  ? 

2204  X  55  X   60   X  12  X  22 


Ans.  90,  or. 


840  X  36  X    7 


To  alter  the  Production. — To  alter  the  length  delivered  : 
Change  the  speed  of  the  whole  by  altering  the  machine  pulleys. 

To  alter  the  weight  delivered :  This  may  be  done  by  allow- 
ing the  length  to  remain  unaltered  or  otherwise ;  in  the  latter 
case  the  weight-unit  of  the  lap  need  not  be  altered,  but  in  the 
former  it  would  be  necessary.  The  weight-unit  of  the  lap  and 
of  the  production  may  be  altered  by  changing  the  draft  or  the 
weight  of  the  feed.  Draft  affects  the  weight  in  the  inverse  pro- 
portion, whilst  change  in  the  weight  of  the  feed  would  act  in 
the  direct  proportion. 

Changes  in  the  draft  of  this  machine  are  not  frequent. 
When  necessary  they  are  confined  to  the  alteration  in  the  draft 
between  the  first  and  third  drawing  rollers. 


80  COTTON   SPINNING   CALCULATIONS 

Exercises  in  Changing  the  Sliveu  Lap  Machine. 

Exercise  1.— With  the  speeds  as  in  the  figure  (17),  what  effect  would  changing 
the  weight  of  the  sliver,  from  30  to  36  grains  per  yard,  have  upon  the  laps 
produced  :  (a)  The  weiglit  per  yard  ?  (b)  The  weight  produced  per  unit  of  time  ? 
(c)  The  length  produced  in  hanks?  Jns.  252  grs. ;  2620  lbs. ;  90  hanks. 

Exercise  2.— What  changes  would  be  necessary  if  the  sliver  used  was  altered 
from  30  grains  to  36  grains  per  yard,  in  order  that  the  weight  and  length  units, 
delivered,  be  unaffected? 

Ans.  Alter  the  draft  change  wheel  to  increase  the  draft : :  30  :  36. 

Exercise  3. — What  changes  would  secure  the  same  weight  per  unit  of  time, 
and  at  the  same  time  alter  the  weiglit  of  the  lap  ^  ?    Ans.  Altering  the  draft  -^. 

Exercise  4. — What  would  be  the  weight  per  yard,  and  of  laps  per  10  hours, 
if  each  lap  measured  280  yards  and  one  minute  is  lost  at  the  completion  of  each  ? 
The  lap  rollers  being  of  the  size  given  in  the  figure,  and  make  20  revolutions 
per  minute ;  each  of  the  fourteen  slivers  fed  weigh  28  grains  per  yard,  and  the 
draft  in  the  machine  is  2-08. 

The  Ribbon  Lap  Machine. 

Fig.  18  represents  some  of  the  principal  parts  and  the 
gearing  in  a  ribbon  lap  machine. 

The  object  of  the  machine  is  :  to  prepare  from  the  sliver  laps 
one  which  has  the  fibres  arranged  in  the  most  suitable  manner 
for  combing  ;  to  make  the  ribbon  of  fibres  uniform  in  thickness, 
width,  and  weight  throughout,  and  with  all  the  fibres  parallel. 

This  machine  consists  of  parts  having  the  following  functions  : 

(a)  The  feed  parts  :  Lap  rollers  3  ins.  diameter,  and  the 
detector  of  missing  and  light  laps  ;  the  latter  is  not  shown. 

(h)  The  rollers  (1]  x  11  X  li  xlJ,)  for  attenuating  the 
ribbon  of  fibres  to  the  extent  necessary,  to  lay  the  fibres  parallel, 
and  to  make  the  ribbon  the  desired  weight. 

(c)  The  curved  folding  plate  C  guides  the  ribbon,  passing 
from  the  rollers,  on  to  the  folding  table  D,  placing  it  upon  the 
latter  at  right  angles  to  the  rollers.  In  the  figure  only  one 
head  is  shown.  The  machine  is  usually  made  with  six  heads, 
to  treat  six  sliver  laps,  and  hence  the  rollers  are  constructed  to 
deal  with  that  number.  There  are,  therefore,  six  curved  folding 
plates,  and  the  folding  table  is  continued  to  the  left  accordingly. 

(d)  The  carrier  and  compressing  rollers,  3  ins.  diameter,  are 
placed  at  intervals  along  the  folding  plate  to  move  forward  the 
folded  ribbons. 


AND   COSTS   OF   YARN 


81 


rrt 

c^ 

o 

in 

ol 

b 

^1 

1 

in 

1 

ci 

cj 

82  COTTON   SPINNING   CALCULATIONS 

(e)  The  calender  rollers  (5"  X  5")  for  smoothing  and 
pressing  the  ribbons  and  completely  uniting  them. 

(/)  The  lap  rollers  (12"  X  12")  for  winding  the  continuous 
ribbon  of  fibres,  or  lap,  tightly  upon  a  wood  roller. 

The  machine  is  driven  by  a  strap  from  a  9-inch  drum  on  the 
line  shaft  which  makes  220  revolutions  per  minute  and  drives 
the  16-inch  pulleys  on  the  machine  shaft. 

The  revolutions  per  minute  of  its  various  parts  are  as 
follows :  — 

T.     n  1  n       /o'/N      iQ.r  220x9x72x25x54x30 

Feed  lap  rollers  (3  )  =  13*5,  or,  — :r^ — wt^ — ^-r^r — — - — — 

^  ^     ^  '      '  16x68x100x70x56 

The   first   draw   roller  \  _  o^  o         220  x   9   X  72  x   25   x  54 
(37-40-70)  I  -  ^5  d,  or,  16  x  68  X  100  x  70 

The  fourth  draw  roller.  _  ,^,  220  x   9   X  72 

(68-25-li")  }  -  ^'^^'  ^^'' 

The   carrier  and  com-  \  _  „-, 
pressing  roller  (22-3")  /  ~  '^'  ^^' 

The  calenders   (21-5")    =  44-25,  or. 
The  lap  rollers  (12"-12")  =  18-55,  or, 


) 

16  X  68 

220  X 

9 

X 

31  X 

22 

16 

X 

54  X 

22 

220 

X 

9 

X  20 

X 

15 

31, 

16 

X  40 

X 

21 

220 

nv  

X 

9 

X  20 

X 

15 

X 

21 

16  X  40  X  21  X  50 
Drafts — 

Between  first  roller  and^  _  ^  ^o        "^^  ^  ^ 
the  feed  lap  roller         /  "  ^'^^'  °^*'  37  x~3 

Between     second    roller  \  _     ^^         37  x  1^ 

and  the  first  roller        /  "  ^''^'^'  °^'  30  X  1| 
Between  third  roller  and  \  _  -...q         30  X  40  x  li 

the  second  roller  /  -  ^''^^'  ^^'  37  x  22  X  li 

Between  third  roller  and  )  _  ^  qo         40  X  li 

the  first  roller  /  -  ^'^^'  °^''  22  x  l| 

Between  fourth  roller  and  I      ^  op         22  x  70  x  100  x  Jj 

the  third  roller  /  "  ^'^^'  ^^>  40  X  54  x   25   xTi 

Between  fourth  roller  and  I  _  ^  -in         "^^  ^  ^^^  ^  ^l 
the  first  roller  /  -  '^'^^>  ^^>  54  x   25   X  ll 

Between  carrier  and  the  ^  _  .  ^  ^         68  x  31  X  22  x  3 
fourth  roller  |  -  1"18,  or,  72  x  54  x  22  x  1| 

Between     calender     and  \      ^  ^.o         22  x  54  X  20  X  15  X  5 
carrier  roller  )  -  ^'^^'  ^r,  22  x  31  x  40  x  21  X  3 


AND   COSTS   OF   YARN  83 

Between  lap  rollers  and  ■»  _  -,  ./^-,      .   21  x  12 
the  calenders  |  ~  ^'^^'  °^*'  50  X   5 

Between  delivery  lap  rollers  and  the  feed  lap  rollers  =  6*05, 
.  76  X  70  X  100  X  68  X  20  X  15  X  21  X  12 
°^''  37  X  54  X    25    X  72  X  40  X  21  X  50  X   3 

Production. — The  weight,  per  unit  of  length  of  the  lap  made, 
is  controlled  by  the  weight  of  the  laps  fed,  and  by  the  total 
draft.  Any  alteration  in  the  latter  items  affect  the  former  in 
the  direct  and  inverse  proportions  respectively,  namely — 

The  heavier  the  feed,  the  heavier  the  lap,  and  vice  versa. 

The  greater  the  draft,  the  lighter  the  lap,  and  vice  versa. 

The  length  delivered  is  only  affected  by  the  alteration  of 
speed  of  the  machine  shaft. 

It  is  customary  to  regulate  the  weight  of  the  lap  by  altering 
the  draft ;   but  sometimes  by  altering  the  weight  of  the  lap  fed. 

The  draft  can  be  altered  to  a  very  considerable  extent  with- 
out influencing  the  quality  of  the  work. 

The  customary  changes  are  made  through :  The  pinion  (54) 
or  the  back-roller  wheel  (70)  for  the  draft ;  the  machine  pulleys 
(16  inches)  for  speed. 

The  restrictions  in  altering  the  draft  and  weight  of  the  feed 
arise  from  the  gross  weight  of  the  laps  J;hat  are  required  for  the 
combing  machines. 

Example  1. — If  this  machine  has  six  heads,  and  the  laps  fed  each  weigh  at 
the  rate  of  202  grains  per  yard ;  what  weight  of  laps  in  pounds  would  be  produced 
in  10  hours'  uninterrupted  working,  and  what  would  be  the  weight  of  these 
in  grains  per  yard  ? 

.       202  X  6      f.^^       .  1 

-4«s,  — -— - —  =  200  grains  per  yard 
6-05  ^  ^     •' 

^^..      12      22      10x60x200      „„„  „ 
18-55  X  3-^  X  y  X .QQQ =  333  lbs. 

EX.UIPLE  2. — What  would  be  the  weight  of  the  laps  per  yard  if  the  draft- 
change  pinion  54  was  changed  to  3G  ?  How  would  this  change  influence  the 
weight  and  length  produced  in  ten  hours  ? 

Ans.  The  draft  would  be  altered  in  the  inverse  proportion  to  the  change 
wheels,  and  hence — 

6-05  X  54  _  q.()7 
36 


84  COTTON  SPINNING  CALCULATIONS 

and  the  weight  per  yard  of  the  lap  produced  would  become  lighter  in  direct 
proportion  to  the  change  in  this  wheel,  and  therefore  — 

200  X  36      ,  „„       .  , 

^2 =  133  grains  per  j^ard 

And  the  weight  produced  in  10  hours  would  be  affected  in  the  same  terms, 
54  :  36,  the  length  remaining  unaffected. 

Exercises. 

1.  The  feed  consists  of  six  heads,  and  the  weight  per  yard  of  the  laps  is  240 
gi-ains,  the  draft  required  being  5.  What  weight  of  lap,  per  yard  and  per  10 
hours,  should  be  produced,  allowing  2^  per  cent,  for  stoppages  ?  Also,  what 
draft  pinion  wheel  would  be  necessary  to  adapt  the  machine,  other  particulars 
being  as  per  Fig.  18? 

2.  If  the  machine  was  producing  laps  weighing  240  grains  per  yard,  geared 
as  in  Fig.  18,  what  would  be  the  average  weight  per  yard  of  the  laps  fed  ? 

3.  Upon  testing  the  weight  of  the  laps  produced,  they  are  found  224  gi-ains 
per  yard  instead  of  240  grains :  what  sizes  of  draft  pinion  or  back-roller  wheel 
would  restore  the  laps  produced  to  their  proper  weight  ?  Also,  give  the  pro- 
portional alteration  that  this  change  would  make  in  the  weight  of  laps  produced 
per  unit  of  time. 

4.  If  the  draft  pinion  54  was  changed  to  60,  what  effect  would  it  have  upon 
the  drafts  between  :  (a)  the  first  and  second  ;  (6)  the  second  and  third  ;  (c)  the 
third  and  fourth  rollers  respectively  ? 

5.  If  the  weight  per  yard  of  the  laps  produced  became  240  grains  instead 
of  200,  what  would  you  suspect,  and  what  would  you  do  ? 


Combing  Machines. 

Fig.  19  represents  the  gearing  in  the  Nasmith  combing 
machine. 

The  object  of  this  machine  is  to  comb  the  fibres  and  reject 
those  that  are  defective  and  below  a  specified  length. 

The  cotton  for  treatment  in  this  machine  is  prepared  from 
the  card  sliver,  by  the  sliver  and  ribbon  lap  machines,  an 
alternative  to  these  processes  being  one  head  of  drawing  followed 
by  the  Derby  Doubler.  The  former  is  the  modern  system,  and 
has  many  advantages  over  the  latter,  the  chief  of  these 
advantages  being  a  reduction  in  the  good  fibres  wasted. 

The  names  of  the  parts  in  the  figure  are  as  follows  : — 

E,  the  lap  rollers, 

F,  the  pawl  actuating  the  lap  roller  gear. 


AND   COSTS   OP   YARN 


85 


CM//" 

Nr.iK 


o 

<N"H — 

CM  CO 


g         "Si 


^■^J» 


86  COTTON   SPINNING  CALCULATIONS 

G,  a  crank  on  the  oscillating  shaft  H. 

HI,  the  oscillating  shaft  for  operating  the  feed  and  the 
advancing  and  receding  movements  of  the  nippers. 

J,  a  lever  coupled  to  the  shaft  HI  at  I. 

K,  a  crank ;  its  stud  and  slide  operate  the  lever  J. 

L,  the  machine  driving  shaft. 

U,  a  cam  on  the  comh  cylinder  shaft. 

T,  a  quadrant  rack  lever  centred  on  HI,  and  actuated  by  a 
stud  and  bowl,  the  latter  projecting  into  the  cam  U. 

E  and  30  is  the  quadrant  rack  pinion  and  spindle. 

47  is  an  escapement  clutch,  the  left  toothed  portion  being 
secured  to  the  spindle  E,  the  right  portion  being  loose  upon 
E,  and  engaged  and  disengaged  with  the  left  portion  to  obtain 
movement  of  the  wheel  containing  47  teeth. 

P,  a  cam  for  controlling  the  clutch  Q. 

V  are  the  detaching  rollers  connected  by  a  train  of  wheels, 
47,  20,  18,  17,  with  the  clutch. 

M,  the  comb  cylinder. 

N,  the  brush  cylinder. 

0,  the  card  cylinder. 

W,  the  head  calender ;  there  is  one  for  each  head. 

30,  25,  17,  20,  are  the  "  draw-box."  The  draw-rollers  are 
four  in  number,  to  attenuate  the  combed  slivers. 

Y,  the  draw-box  calender. 

Z,  the  coiler  delivery  rollers,  and  the  coiler  and  can  wheels 
are  shown  beneath. 

The  speed  of  the  comb  cylinder  in  this  machine  ranges  from 
90  to  100,  according  to  the  quality  of  staple  treated.  This 
machine  is  especially  adapted  for  combing  the  shorter  staples 
from  the  equivalent  of  G.  Middlings  American  and  upwards. 
Another  feature  of  the  machine  is  the  wider  range  of  selection  in 
respect  of  the  length  of  the  fibres  rejected.  With  good  staples 
this  can  be  reduced  to  as  low  as  12  per  cent,  without  interfering 
with  the  thoroughness  of  the  combing.  The  piecing  is  accom- 
plished on  a  much  better  principle,  and  the  adjustments  are  all 
much  simpler  than  in  the  machines  constructed  on  the  Heilmann 
system.     The  production  is  also  considerably  greater. 

The  following  are  the  speeds  of  the  various  parts  and  manner 


23  X  90 

100  X  90  X  24 

23  X  20 

.  100  X  25  X  1 

25  X  32 

100  X  4  X 

42 

X 

35 

75  X 

80 

X 

47 

lOOx  5  X 

42 

X 

35 

^^'      75  X 

80 

X 

47 

AND   COSTS   OF    YARN  87 

of  ascertaining  them  by  calculation  when  the  comb  cylinder  makes 
100  revolutions  per  minute  : — 

Machine  pulley  =  391/.  :  ^-^^^^ 
Cam  shaft  =  100  :i^^-^^|^A|B 

Brush  cylinder  =  470  : 

Card  cylinder  =  3125 
Lap  Rollers. 

Assuming  the  pawls  to  move  \ 

four  teeth  per  revolution  (  =  2*085 
of  the  comb  cylinder  ) 

Ditto  five  teeth  ditto  =  2-606 

Note.— The  number  of  teeth  moved  bj^  the  pawls  may  be  adjusted  to  give 
the  desired  length  of  feed.  This  is  the  medium  of  altering  the  draft.  There 
are  two  pawl  levers,  one  actuating  the  feed  and  the  other  the  lap  rollers,  in  a 
similar  manner,  but  separately  driven. 

Detaching  Rollers.— These  are  actuated  through  the  medium 
of  the  quadrant  rack  and  escapement  clutch,  the  movement  of 
the  former  being  communicated  to  the  rollers  only  when  the 
latter  is  closed.  The  quadrant  moves  up  and  down  seventeen 
teeth  each  revolution  of  the  comb  cylinder.  The  clutch  escape- 
ment is  open  during  a  period  amounting  to  eight  teeth  of  the 
upward  movement  of  the  quadrant  rack.  At  this  point,  in 
the  upward  movement,  the  latter  makes  a  pause  to  enable 
the  escapement  clutch  to  be  closed,  and  then  it  resumes  the 
upward  movement.  This  has  the  effect  of  turning  the  detaching 
rollers  backward  to  the  extent  of  nine  teeth  of  the  movement  of 
the  quadrant  rack.  The  clutch  remains  closed  during  the  whole 
of  the  downward  movement,  and  hence  the  detaching  rollers  are 
moved  backward  nine  teeth  and  forward  seventeen  teeth  of  the 
quadrant's  action.  The  pinion  engaging  the  quadrant  rack  con- 
tains thirty  teeth,  and  therefore  makes  ^  of  a  complete  oscillation 
each  revolution  of  the  comb  cylinder ;  s%  and  Ifj  of  this  move- 
ment are  therefore  utilized  in  turning  the  rollers  backward  and 


88  COTTON   SPINNING  CALCULATIONS 

forward,  respectively.    Hence,  these  movements  result  in  the  first 

9   X  47  17  X  47 

detaching  roller  moving  ^ — ^-.  backward,  and  ^ — ^  forward, 

respectively,  per  revolution  of  the  comb  cylinder.  This  amounts 
to  the  following  rates  per  minute  : — 

Backward, ;^ ^  =  70 "5  revolutions 

„          ^   100  X  17  X  47      ,„.,,  ,   ,. 

Forward,  — ^rr -^  =  133^-  revolutions 

oU  X  Ay) 

the  forward  progress  per  minute  amounting  to  (133^  —  70"5)j"o 
X  52-  =  177"-2. 

The  second  detaching  roller  exceeds  the  movement  of  the 
first  as  18  :  17  on  account  of  the  gear. 

These  amounts  must  be  regarded  as  fixed,  as  adjustments  of 
this  gearing  are  not  arranged  for. 

The  combing  head  calenders  are  2f  inches  in  diameter,  and 
make  19*947  revolutions  per  minute — 

100  X  48  X  43  X  40  X  16  X  17  X  33  X  20 

24  X  40  X  50  X  25  X  43  X  72  X  20 

The  revolutions  per  minute  of  the  first  draw  roller  =  58'645— 

100  X  48  X  43  X  40  X  16  X  17 
24  X  40  X  50  X  25  X  30 

The  revolutions  per  minute  of  the  second  draw  roller 
=  70-374— 

100  X  48  X  43  X  40  X  16  X  17 
24  X  40  X  50  X  25  X  25 

The  revolutions  per  minute  of  the  third  draw  roller  =  110 — 

100  X  48  X  43  X  40  X  16 
24  X  40  X  50  X  25 

The  revolutions  per  minute  of  the  fourth  draw  roller 
=  277-42— 

100  X^  48  X  43  XjlO 
24  X  4'0~xl^l 


AND   COSTS   OF   YARN  89 

The  revolutions  per  minute  of  the  draw-box  calender  =  126 — 

100  X  48  X  43  X  40  X  20 
24  X  40  X  31  X  44 

The  revolutions  per  minute  of  the  coiler  delivery  rollers 
=  179-43— 

100  X  48  X  43  X  40  X  70  X  20  X  20 
24  X  40  X  55  X  61  X  20  X  20 

The  revolutions  per  minute  of  the  coiler  =  52-16  ; 
„  ,,  can      =    6-94 — 

100  X  48  X  43  X  40  X  70  X  20  x  13  X  18  X  18 
24  xlOlTSS^X  61  X  20  X  3^"x¥6  X  84 

The  drafts  between  the  parts  in  progressive  order  work  out 
as  follows : — 

(a)  Lap  and  first  detaching  roller  by  gear  direct.  The 
progressive  movement  in  respect  of  the  detaching  roller  amounts 
to  17  -  9  =  8  teeth  of  the  quadrant  wheel,  or  o^^  of  the  47 
clutch  wheel  which  drives  that  roller,  per  revolution  of  the 
comb  cylinder,  and  therefore — 

-  „- — 90  =  ^^®  progressive  movement  or  the  amount  gained  in 
revolutions  of  the  detaching  roller  per  revolution 
of  the  comb  cylinder  or  per  nip. 

The  movement  of  the  lap  rollers  train  of  wheels  is  derived 
from  a  pawl  moving  the  ratchet  wheel,  75,  a  certain  number 
of  teeth  each  nip ;  the  extent  of  this  movement  can  be  varied, 
and  is  one  medium  of  tensioning  the  lap.  The  feed  roller  is 
not  shown,  but  it  is  also  worked  by  a  pawl  and  ratchet,  the 
pawl  being  operated  each  nip,  and  the  ratchet  wheel  is 
secured  upon  the  feed  roller.  The  movement  of  the  feed  roller 
is  adjusted  in  altering  the  draft.  If  the  pawl  is  moved  four 
teeth  per  nip  or  revolution  of  the  comb  cylinder,  the  movement 
of  the  lap  rollers  per  nip  will  be  the  denominator  in  the 
succeeding  calculations.     Hence  the  draft — 


90  COTTON   SPINNING   CALCULATIONS 

(a)  By  gear  direct — 
8  X  47  X  9'^ 

^  30x20x10  ^  8  X  47  X  9  X  75  X  80  X  47  X  4  _ 

4  X42X35         ,,,     30X20X10X  4  X42X35~X  11  ~^'^^ 

75  X  80  X  47        ^ 

(b)  By  calculated  surface  speeds  per  minute— 

The  draft  between  the  first  and  second  detaching  rollers  — 

('')  =  }-f[:|  =  1-058 

The  draft  between   the  second    detaching   rollers  and   the 
combing  head  calenders — 

48x43x40x16x17x83x20 
^  24  X  40  X  50  X  25  X  43  X  72  X  20  ^  ^ 
8  X  47x18  X  9 
30x20x17  xlO 
=  48x43x40xl6x  ITx  33  X  20  X  11x30x20  x  17  x  10 
24  X  40  X  50  X  25  X  43  X  72  X  20  X  4  X  8  X  47  X 18  x"9 
=  0-916 
1 72"4 
<'')         =187^8=  O-^lS 

The  draft  between  the  combing  head  calenders  and  the  first 
draw-head  roller — 

(a)  =  20X72X43X  li  _ 
"^  ^  20x33x30x21  ~  ^"^^ 

W  ^  207:35  ^ 
^  ^  172-4        ^  ^ 

The  draft  between  the  first  and  second  draw-head  rollers — 

,  ,  30X9X8      ,  ^ 

(^^  =28^8X9  =  ^"'^ 

n\  248-82      ^^ 

^'^  =  207^5  =  ^'^ 


(«) 


AND   COSTS   OF   YARN  91 

The  draft  between  the  second  and  third  draw-head  rollers — 
/  N  30  X  9  X  8      .  _  _ . 

^«>  =  I7x¥x9  =  ^'^^' 

^^  ~  248-82 

The  draft  between  the  thh-d  and  fourth  draw-head  rollers — 

(b)  =  i^^  =  2-79 

^^^  389-21      ^  ^^ 

The  draft  between   the  fourth  draw-head    roller  and  the 

subsequent  calender — 

/  N  20  X  2|      , 

1089       . 
^^>  =  1089  =  ^ 

The  draft  between  the  draw-head  calender  and  the  coiler 
delivery  rollers — 

.  .  _  44  X  31  X  70  X  20  X  20  x  2    _ 

^""^  ~20x55x61x20x20x2i~-^^'^^ 

(^>         =  w  =  '■''' 

The  draft  between  the  lap  rollers  and  the  coiler  delivery 
rollers,  when  the  pawl  moves  4  teeth  per  nip — 
48  X  43  X  40  X  70  X  20  X  20 


.  ,  24  X  40  X  55  X  61  X  20  X  20 

(a)      = 


X2 


4  X  42x35     ^„ 
X2J 


75X80X47 

^  48x43x40x70x20x20x  2  X  47x80x75 
24  X  40  X  55  X  61  X  20  X  20  X  2j  X  35  X  42  X  4 

=  62-58 

Draft  between  the  lap  and  coiler  delivery  rollers  when  the 
pawl  moves  the  feed-ratchet  wheel  5  teeth  and  8  teeth 
respectively — 

(«)  =  "^  =  50-08 


92  COTTON   SPINNING  CALCULATIONS 


(i)  =  ^iS?  =  31-29 


By  proportion — 
By  proportion — 


36-04 

62-58  X  4 

5 

62-58  X  4 

=  50-07 


=  31-29 


The  percentage  of  waste  at  this  machine  is  rarely  lower  than 
14  per  cent.  If  15  per  cent,  be  allowed,  and  the  weight  of  the 
laps  per  yard  be  each  taken  as  28  dwts.,  a  machine  with  4  heads 

...      28  dwts.  X  24  grs.  X  4  heads  ^   85 
would  produce  a  sliver  weighmg fi2^^8 lOO 

when  the  feed  pawl  moves  4  teeth  per  nip  =  36-51  grs.  per  yard. 

28  X  24  X  4 
And  when  the  feed  is  actuated  5  teeth  per  nip, kTvau" 

^  100  ^  45-62  grs.  per  yard. 

Note. — The  length  fed  of  lap  per  nip  when  the  pawl  moves  8  teeth  would  be 

The  latter  length  would  prove  in  most  cases  an  impracticable 
amount  in  this  machine.  It  would  make  the  combing  action 
very  severe,  throwing  a  great  deal  more  work  on  the  top  comb 
than  it  is  capable  of  accomplishing.  Another  way  of  adjusting 
the  draft  in  this  machine  is  by  changing  the  wheel  compounded 
with  the  feed  ratchet  wheel ;  this  may  be  called  the  draft 
change  wheel.  Altering  this  wheel  will  alter  the  draft  in  the 
inverse  ratio,  because  it  will  reduce  the  length  feed  when  it  is 
reduced  in  size.  Changes  in  the  weight  of  the  sliver  and  the 
output  of  the  machine  may  be  accomplished  by — 

(a)  The  draft  is  altered  by  the  wheel  coupled  with  the  ratchet 
wheel,  or  by  increasing  the  radius  of  the  pawl  lever. 

Note. — This  wheel  can  only  be  altered  to  a  limited  extent,  owing  to  its  alter- 
ing the  ratio  between  the  lap  and  the  feed  rollers ;  unless  the  pawl  lever,  operating 
the  latter,  is  altered  at  the  same  time.  The  lap  is  liable  to  be  unduly  stretched 
or  puckered  if  this  is  not  done. 


AND  COSTS   OF   YAEN  93 

(b)  Altering  the  weight  of  the  lap. 

(c)  Altering  the  length  delivered  by  changing  the  speed 
of  the  machine. 

The  production  in  hanks  and  pounds  per  week  of  a  Nasmith 
machine  geared  as  in  the  figure  and  having  four  heads,  the 
comb  cylinder  making  100  nips  per  minute,  using  laps  28  dwts. 
per  yard,  the  draft  62*58,  15  per  cent,  being  lost  in  strips, 
time  lost  10  per  cent.,  engine  time  55  hours  per  week,  would 
be  computed  as  follows  : — 

55  X  90   X  60  _  (minutes     worked    per    week 
100  ~  i  less  allowances 

55  X  90  X  60  X  179-43  X  2"  x  22  ^  i  inches  delivered  per  week  by 
^110  7  ~  ^  the  coiler  delivery  rollers 

55  X  90  X  60  X 179-43  x  2"  x  22  ^  j  hanks  delivered  per  week  by 
100  X  840  X  36  7         1  the  coiler  delivery  rollers 

=  110-82 

Percent.  Revs.  P.M.     Dia.  HrB.    Mins.      [yards  delivered  by  the 

90  X  179-43  X  2^^  X  22  X  55  X  60  ^     coiler  delivery  rollers 

100  X   36"  7  (  per  week,  less  stoppages 

Grs.        D«t8.    Laps.  Percent. 

24  X  28  X  4  X  85  _  j  weight  of  the  sHver  in 
6258    X    100  ~  I  grains  per  yard 

Draft. 

Weight  in  pounds  of  the  sliver  delivered  by  the  machine  per 
week  of  55  hours,  no  allowance 

24  X  28  X  4  X  85  X  17943  X  2  X  22  X  55  X  90  X  60 


62-58   X    100  X  36        x     7     X     100x7000 


=  485-3 


The  production,  in  case  the  feed  pawl  moved  5  teeth  per  nip 
instead  of  4,  would  be — 

Weight  of  the  sliver  per  yard  when  pawl  moved  4  teeth — 

4  X  28  X  24       85       ^^  „ 

62-58         ^  100  =  ^^"^  ^^^^^^ 

Weight  of  the  sliver  per  yard  when  the  pawl  moves  5  teeth — 
_  365  X  5  _  ^^.^ 


94  COTTON   SPINNING   CALCULATIONS 

Production  in  pounds  per  week  of  55  hours — 

485-3  X  5      ^^^  .  ,, 

=  606*5  lbs. 

4 

The  length  delivered  after  the  alteration  would  be  the  same, 
but  the  length  fed  would  be  one  quarter  more,  and  therefore  the 
weight  delivered  would  be  proportionately  increased. 

The  production  per  week,  if  the  feed  pawl  moved  the  lap 
rollers  8  teeth,  would  be — 


485-3  X  8 


lbs.  =  970-6 


Exercise  1. — Assuming  the  speed  of  the  comb  cylinder  100  revolutions  per 
minute,  and  the  machine  puUej's  14  inches  in  diameter  are  changed  to  12i  inches, 
what  would  be  the  speeds  of  each  of  the  parts  of  the  machine  ? 

Ansiver — 

Lap  rollers  with  the  pawl  moving  4  teeth     2-335 

,,                ,,                „            0    ,,  o'oob 

First  detaching  roller,  backward  .     .     .  78'96 

„            „           „       forward    .     .     .  149-146 

Second      „          ,,       backward.     .     .  83-0 

„            ,,          „       forward    .     .     .  157-92 

Cam  shaft 112 

Comb  cylinder 112 

Machine  shaft 4382% 

Brush  cylinder 404*5 

Card          „ 3-5 

Combing  head  calenders 23-936 

First  drawing  roller 65-082 

Second        „             78-818 

Third           „             123-29 

Fourth         „             310-71 

Draw-box  calender 141-12 

Coiler  delivery  roller 200-96 

Coiler 58-42 

Can 7-77 

Exercise  2. — What  would  be  the  consumption  of  laps  and  production  of  sliver, 
in  hanks  and  pounds,  per  50  hours'  uninterrupted  working  of  a  Nasmith  comber, 
and  the  weight  of  the  lap  per  yard  ;  also  the  percentage  of  the  waste  extracted, 
under  the  folloAving  conditions  ? — 

Sliver  produced  in  1  minute,  1117  grains. 
Strips  ,,  ,,  292  grains. 


AND    COSTS   OF   YARX  95 

Weight  of  the  sliver,  40  grains  per  yard. 
Number  of  combing  heads,  4. 
Draft  in  the  machine,  50. 

Ansiver — 

Length  of  lap  in  hanks  =  8*328 

Weight  of  laps  in  pounds  =  G24'8 

Length  of  sliver  in  hanks  =  104"1 

Weight  of  sliver  in  pounds  =  499'7 

Percentage  of  waste  =  20 
Weight  of  the  lap  per  yard  =  649  grains. 

Exercise  3, — Calculate  the  amounts  of  the  laps  consumed  and  the  sliver 
produced,  in  hanks  and  pounds,  if  the  pawl  moved  5  teeth  instead  of  4, 
assuming  the  latter  gives  625  lbs.  weight  of  sliver,  and  the  other  conditions  as 
given  in  the  answer  to  the  previous  question. 

625_^x^5^3^^^3^.2^jj^^_,^^^^ 

^'^^^  ^  ^  =  10-41  hank  of  lap 
4 

The  length  of  the  sliver  would  be  unaltered. 

The  weight  of  the  sliver  would  be  • ^ =  624-6  lbs. 

Exercise  4. — What  would  be  the  consumption  of  laps  and  the  sliver  produced, 
in  hanks  and  pounds,  per  50  hours'  uninterrupted  working  in  a  Nasmith  comber ; 
also,  the  percentage  of  the  waste  made  when  the  conditions  are  as  follows  ? — 

Production  in  one  minute,  1120  grains  of  sliver  ;  strips,  280  grains  ;  weight  of 
one  yard  of  sliver,  40  grains ;  number  of  combing  heads,  4 ;  draft,  50. 

Answer —  Sliver  Laps 

Hanks  per  week ....     100  8 

Pounds        „        ....    480  600 

Percentage  of  the  waste,  20 

Fig  20  represents  the  gearing  in  a  single  acting  combing 
machine  on  the  Heilmann  system. 

The  object  of  this  machine  is  to  comb  the  fibres  and  reject 
those  that  are  defective  and  below  a  specified  length. 

The  cotton  is  prepared  for  this  process  in  the  same  manner 
as  that  for  the  Nasmith  combing  machine,  the  range  in  the 
weight  of  the  laps  for  the  Heilmann  being  from  200  to  400 
grains  per  yard,  and  for  the  Nasmith  about  double  that 
weight. 

The  actions  in  these  two  types  of  combing  machines  differ, 
fundamentally,  in  that  the  fibres  in  the  Nasmith  machine  are 


96 


COTTON   SPINNING   CALCULATIONS 


only  submitted  to  once  combing,  whereas  in  the  Heilmann  they 
are   submitted  a  number  of  times,  their  introduction  to  that 


action  being  graduated.     The  effect  of  this  is  that  the  Heihnann 


AND  COSTS  OF  YAllN  97 

wields  greater  powers  of  discrimination  in  respect  of  the  length 
and  other  features  of  the  fibres  selected  by  it. 

The  respective  parts  are  named  as  given  in  the  figure.  The 
revolutions  of  the  comb  cylinder  range  from  60  to  90  per  minute. 
This  is  often  spoken  of  in  terms  of  nips  instead  of  revolutions, 
there  being  one  nip  or  complete  cycle  of  actions  per  revolution 
of  the  comb  cylinder  in  the  single  acting  type.  In  the  Duplex 
type  the  cycle  of  actions  are  accomplished  in  each  half  revolution 
of  the  comb  cylinder. 

The  following  is  the  mode  of  calculating  the  speeds  of  the 
various  parts,  for  this  purpose  the  comb  cylinder  being  assumed 
to  make  80  revolutions  per  minute  : — 

Eevolutions     of     machine  \  _  on^i  o      ,   80x80 
pulley  per  minute  '  ~        - 1 '  °^ '      ^21 

Eevolutions  of  lap  rollers!       .  ,  80  x  1  X  18  X  21  X 20  x 30 

per  minute  /  -  1  7  /,  or,  ^  x  38  X  20  X  55  X  49 

Eevolutions  of  feed  roller  ^  _  80  x  1  x  18 

per  minute  J  ~  *'^^>  °^'  5  X  38 

Eevolutions  of  comb  head  ^  _  . . .  -  <.      .   80x80x  2  x20 
calenders  per  minute       }  ~  ^^-^^^  or,  80  X  14  x  20 

Eevolutions  of  first  roller]  80  X  25  X  14 

in     the    draw-box    perl  =  23*33,  or,  ^       .„ 

minute  J  ^5X4H 

Eevolutions  of  third  roller  80  x  25  X  50  x  40 

m    the    draw-box     per  >  =  104-5,  or,  ^ — -t-z — ^ 

minute  )  Z5  X  45  X  d4 

Eevolutions    of    draw-box  |  _  ^  80  x  25  x  50  x  40  X  22 

calender  per  minute        i  -  ^i  ^>  or,  ^^  x 45  X  34  x  40 

Eevolutions  of  coiler  de-  -i  _  o-i . «         80  x  GO  X  22  X  18 
livery  rollers  per  minute  f  ~  ^^  ^>  o^"'  59  x  22  X 18 

Eevolutions       of      brush  \  80x34x80 

cylinder  per  minute         •'  "~  '  °^''  25^^1 

Eevolutions  of  card  cylin-j  _  80  x  1 

der  per  minute  /  —  z  5,  or,  ^ 

Drafts — 

Between  lap  and  feed  rollers  =  1166, 
49  X  55  X  20  X  1 


or, 


30  X  20  X  21  X  25 

H 


98  COTTON  SPINNING  CALCULATIONS 

Between  lap  and  comb  head  calenders  =  6'45, 

49  X  55  X  20  X  38  X  5  X  80  X  2  X  20  X  2f 

or — — -- 

'  30  X  20  X  21  X  18  X  1  X  80  X  14  X  20  X  2^ 

Between  lap  and  first  draw  roller  =  6*58, 

49  X  55  X  20  X  38  X  5  X  25  X  14  X  If 

or    5. 

'  30  X  20  X  21 X  18  X 1  X  25  X  48  X  2| 

Between  lap  and  third  draw  roller  =  29*51, 

49  X  55  X  20  X  38  X  5  X  25  X  50  X  40  X 12 

or - 

'  30  X  20  X  21  X  18  X  1  X  25  X  45  X  34  X  2f 

Between  lap  roller  and  draw-box  calender  =  32*5, 

49  X  55  X  20  X  38  X  5  X  25  X  50  X  40  X  22  X  2| 
'  30  X  20  X  21  X 18  X  1  X  26  X  45  X  34  X  40  X  2| 

Between  lap  and  coiler  delivery  rollers  =  33*4, 

_  49  X  55  X  20  X  38  X  5  X  60  X  2  X  22 

or, 

'  30  X  20  X  21 X 18  X 1 X  59  X  22  X  2f 

Between  first  and  second  draw  rollers — 

Miiil  =  1-24 
25  X  If 

Between  first  and  third  draw  rollers — 

48x50x40xlf       ,  ,^ 

— =  4*48 

14x45x34xlf 

Between  second  and  third  draw  rollers — 

25  X  48  X  50  X  40  X  If  _  q  p 
31xl4x45x34xlf  ~ 


Between  third  draw  roller  and  draw-box  calender — 
=  1-1 


22x2f 


40xlf 


Between  draw-box  calender  and  the  coiler  delivery  rollers- 
40  X  34  X  45  X  25  X  60  X  22  X  18  X  2 


22  X  40  X  50  X  25'x  59  X  22  X  18  X  2| 


=  1-025 


The  movement  of  the  detaching  rollers  is  derived  as  follows  : 
The  quadrant  rack  is  a  part  of  a  lever  actuated  by  a  bowl  pro- 
jecting from  it  into  a  cam.     The  rising  and  falling  movement 


AND   COSTS   OF   YAKN  99 

of  the  quadrant  rack  is  about  12  teeth,  so  that  the  14  wheel 
receives  movement  equal  to  |f  of  a  revolution  per  (nip)  revolu- 
tion of  the  cam  shaft.  The  cam  on  the  left  hand  engages  and 
disengages  the  escapement  clutch,  and  by  this  means  the 
difference  in  the  extent  of  the  backward  and  forward  rotation 
of  the  detaching  rollers  is  obtained.  The  clutch  is  open  during 
the  first  five  teeth  of  the  upward  movement  of  the  quadrant 
rack ;  after  that  movement  the  quadrant  rack  pauses  to  allow 
the  clutch  to  be  engaged,  and  upon  the  resumption  the  detaching 
rollers  commence  their  backward  movement — this  is  a  constant 
amount,  and  is  equal  to  seven  teeth  of  the  rack  pinion.  The 
clutch  remains  engaged  during  the  whole  of  the  downward  move- 
ment of  the  rack,  and  therefore  the  backward  and  forward  move- 
ments of  the  detaching  roller  amount  to  -^  and  1 1  of  a  revolution 
respectively.  This  difference  in  the  movements  is  insufficient  to 
provide  the  necessary  overlay  for  piecing.  Further  variations 
are  obtained,  to  any  extent  within  these  limits,  by  deferring  the 
placing  of  the  leather  detaching  roller  upon  the  fluted  segment 
until  the  length  of  those  fibres,  already  within  the  nip  of  the 
detaching  roller,  project  only  sufficent  for  the  necessary  overlap. 

It  must  be  noticed  that  variations  in  the  overlap  cannot  be 
obtained  by  altering  the  timing  of  the  closure  of  the  clutch  cam. 
The  clutch  cam  can  only  be  satisfactorily  closed  at  the 
moment  that  the  pause  occurs  in  the  upward  movement  of  the 
quadrant  rack.  Closure  at  any  other  period  will  result  in 
damage  to  the  clutch. 

Notes  respecting  the  Permissible  Adjustment  in  the  Drafts. — 
The  drafts  between  the  lap  and  feed  rollers,  detaching  rollers 
and  head  calenders,  head  calenders  and  first  draw  rollers,  third 
draw  roller  and  draw-box  calender,  draw-box  calender  and  the 
coiler  delivery  rollers,  must  always  be  such  that  the  cotton  is 
in  slight  tension  without  straining. 

The  point  admitting  of  variations  in  the  draft  is  therefore 
between  the  feed  and  detaching  rollers.  Alterations  in  this 
alter  the  character  of  the  combing,  because  it  is  accomplished 
by  introducing  the  fibres  more  or  less  gradually,  and  hence 
the  number  of  combing  actions  which  they  are  subjected  to  is 
altered  thereby. 


100  COTTON   SPINNING   CALCULATIONS 

Feeding  a  considerable  length  of  lap  generally  results  in 
greater  waste ;  hence,  light  laps  and  low  drafts  together  are 
not  beneficial. 

Moderately  high  drafts — provided  the  fringe  of  the  lap  is  well 
held  by  the  nippers  and  the  more  numerous  combings  are  not 
injurious — are  conducive  to  better  selection  of  the  fibres. 

The  weight  a  machine  is  required  to  comb  always  decides 
the  count  of  the  combed  sliver. 

The  length  of  the  staple  decides  the  suitable  speed. 

Eesults  must  always  decide  the  weight  of  the  lap  as  its  state 
as  well  as  that  of  the  machine  differ  so  much. 

The  waste  made  ranges  from  15  per  cent,  upwards,  according 
to  the  state  of  preparation  of  the  laps,  the  amount  of  short  fibre 
which  it  contains,  and  the  settings. 

With  laps  each  weighing  240  grains  per  yard,  a  machine, 
containing  six  combing  heads  and  a  total  draft  of  33"4,  the  loss 
in  waste  being  18  per  cent.,  would  make  sliver  weighing — 

240  X  6       82        „„  „        .  , 

-  33.^     ^  100  "^  ^^^^^  ^^^  ^ 

The  percentage  of  the  waste  is  always  based  upon  the  weight 
of  the  feed. 

The  weight  of  the  waste  and  of  the  sliver,  delivered  per 
unit  of  time,  together,  equal  the  weight  of  the  cotton  fed  in  that 
time. 

These  machines  usually  contain  six  or  eight  combing  heads, 
and  therefore  the  amount  fed  is  always  that  number  multiplied 
by  the  average  weight  per  unit  of  length  of  the  lap  fed,  whilst 
the  length  delivered  exceeds  that  fed,  in  one  head,  in  the  terms 
of  the  total  draft. 

Exercise  1. — The  sliver  and  the  waste  produced  in  a  given  time  weigh 
respective!}'  520  and  130  grains,  the  waste  discharged  by  the  six  combing 
heads  weighing  20,  20,  21,  22,  23,  and  24  grains.  Give  the  individual  and  total 
percentage  of  the  loss  at  each  head. 

Exercise  2. — The  sliver  produced  by  a  combing  machine  having  six  heads 
is  at  the  rate  of  8  lbs.  per  head  per  10  hours.  The  total  draft  is  32,  and  the  waste 
made  in  that  period  weighs  10'2  lbs.  What  is  the  percentage  of  the  waste  made, 
the  weight  in  pounds,  and  the  length  in  yards  of  the  laps  consumed  ? 


AND   COSTS  OF   YARN 


101 


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T— 1 

102  COTTON  SPINNING  CALCULATIONS 

Exercise  12. — If  the  machine  pulleys  in  the  last  question,  15  inches  in 
diameter,  are  changed  to  16  inches  in  diameter,  what  difference  in  the  weight  of 
combed  sliver,  waste,  and  laps  would  result  ? 

The  Drawing  Fkame. 

The  object  of  this  process  is  the  elimination  of  the  irregu- 
larities, found  in  the  weight  of  the  sliver,  at  this  stage.  This  is 
accomplished  by  repeating  the  process  of  aggregation  and 
attenuation.  In  this  process  there  are  usually  three  repetitions, 
but  sometimes  two  or  four  are  adopted,  the  former  in  coarse,  and 
the  latter  in  fine,  work.  Eepetition  of  the  process  should  be 
discontinued  when  the  desired  standard  of  uniformity  is  attained. 
The  heads  are  numbered  corresponding  with  the  repetitions 
respectively.  Thus  a  draw  frame  of  three  heads  means  that  the 
cotton  is  treated  to  aggregation  and  attenuation  three  times, 
namely:  in  the  first,  second,  and  third  heads.  It  is  necessary 
to  test  the  sliver,  preferably  at  the  last  head,  at  frequent  and 
fixed  intervals,  four  times  per  day  at  least,  so  that  any  deviation 
from  the  standard  weight  may  be  detected  and  dealt  with.  The 
tests  should  be  recorded  along  with  the  precautionary  or  correc- 
tive measures  taken  in  instances  of  variation.  In  these  tests, 
5,  6,  or  15  yards  will  be  found  convenient  lengths  to  wrap.  The 
sliver  tested  should  be  taken  in  a  manner  ensuring  correct 
representation  of  the  prevailing  condition,  the  best  way  being 
to  take  a  little  from  each  delivery,  but  not  off  full  cans.  The 
weight  is  liable  to  frequent  variation  at  this  stage  ;  the  cause  of 
this  is  not  always  apparent.  The  variations  foreshadow  the 
working  qualities  of  the  cotton  and  irregularities  in  the  treat- 
ment prior  to  this  stage. 

When  variations  are  disregarded,  more  than  corresponding 
differences  may  be  expected  in  the  subsequent  processes,  and 
often  complications  of  an  involved  character  arise  through 
these  faults  being  unchecked. 

During  very  dry  weather  the  wrappings  tend  to  the  heavy 
side.  A  sudden  change  in  the  atmosphere  will  sometimes 
necessitate  an  alteration  of  quite  a  few  teeth  in  the  change  wheel. 
Changes  in  the  mixing  which  result  in  the  cotton  differing  are 
similarly  liable.     Cottons  which  are  softer  than  usual  should 


AND  COSTS  OP  YARN 


103 


be  kept  on  the  heavy  side,  and  vice  versa.  It  is  also  advisable 
to  keep  the  change  wheel  as  large  as  convenient.  By  noting 
at  the  commencement  of  new  mixings  the  quantities  and 
character  of  the  new  lots  of  cotton  contained  in  them,  the 
space  occupied  by  the  scutcher  laps,  and  the  waste  made  in 
carding,  it  is  possible  to  discern  features  that  are  likely  to 
develop  in  the  subsequent  stages.  These,  together  with  the  tests 
of  the  sliver  at  the  third  head  of  the  drawing-frame  provide 
a  good  index  of  the  subsequent  working  capacities  of  the  cotton. 
The  cans  should  be  "  put  up  "  systematically  at  the  feed  of 
each  head,  the  aim  being  to  obtain  like  conditions  at  each 
delivery.  **  Putting  up  "  more  than  one  full  can  per  delivery  is 
detrimental. 


Fig.  21. 


Calculations  relating  to  Draw  Frames  (Fig.  21). — Drafts  between 
the  Various  Parts. — Lifting  roller  A  and  No.  1  draw  roller — 

^Qxlt  _  1.047 
21  X  Ij  -  ^  ^-^^ 


104  COTTON  SPINKING  CALCULATIONS 

Nos.  1  and  2  draw  rollers — 

18  X  If      ^  '^'^ 
Nos.  2  and  3  draw  rollers — 

MA^J^.ii  -  1-925 
25  X  16  X  If  ~  ^  ^^^ 

Nos.  1  and  3  draw  rollers — 

^^  ^^  =  2-67 
16  X  !■•      ^' 

Nop.  3  and  4  draw  rollers — 

16  X  100  X  100  X  1 


47  X   60   X   20   X  11 


=  3-12 


Nos.  1  and  4  draw  rollers- 


100  X  100  X  1|  _ 

60  X   20   X  1|~       "* 

No.  4  draw  roller  and  coiler  delivery  roller  E- 

22  X   3 


48  X  If 


=  1 


Lifting  roller  and  coiler  delivery  rollers,  A  and  E,  the  total 
draft — 

20  X  100  X  100  X  22  X  3^^  _  o  7^^ 

21  X   60   X  20   X  48  X  1 1"  ~     "^ 

There  is  much  difference  of  opinion  in  regard  to  the  system 
of  allocating  the  draft  in  the  draw  rollers  of  drawing  frames 
which  gives  the  best  results.  The  following  has  proved  a  good 
rule,  and  is  in  accordance  with  the  working  conditions : — 

Draft  between  first  and  second  draw  rollers :  not  more  than  1*2 
,,  second  and  third 


V- 


draft  between  first  and  fourth 


1-2 

„  third   and  fourth   draw  rollers :    (draft  between 

the  second  and  third  rollers)^. 

Example. — TIuir,  if  the  total  draft  in  the  draw  rollers  =  x,  and  that  between 


AND   COSTS   OF   YAKN  105 

the  first  and  second  .Xj,  that  between  the  second  and  third  x^,  and  that  between 
third  and  fourth  x-^  {x  in  the  figure  =  8'33) — 

then,  cc  =  ajj  X  ir2  X  x^ 

since  Xj  =  1'2 

a;       8-33 
,'.  «2  X  X3  =  p^  =:  j.^  =  6-95 


The  draft  a'a  is,  in  most  makes  of  these  machines,  incou- 
venieut  for  changing.  Changes  in  this  are  only  necessary  when 
the  total  draft  referred  to  becomes  abnormal.  With  this  draft 
a?2  regarded  as  fixed,  the  defects  arising  are  through  the  draft  Xo, 
approaching  in  amount  that  of  x^ ;  when  the  total  roller  draft  is 
reduced  to  4"38,  then  x^  and  x^  are  alike. 

It  must  not  be  inferred  from  the  latter  statement  that  a 
change  of  the  draft  between  the  first  and  third  rollers  is 
advocated  whenever  the  total  roller  draft  is  altered.  It  is  only 
desired  to  point  out  the  error  arising  when  considerable  change 
is  made  in  the  total  draft,  and  the  expediency  of  affording  relief 
by  a  slight  alteration  in  the  draft  between  the  first  and  third,  in 
order  to  redistribute  the  drafts  in  reasonable  proportions. 

It  is  necessary  also  to  draw  attention  to  the  desirability  of 
using  change  wheels  of  moderate  size,  avoiding  small  ones. 

The    revolutions    of  1   _  22  X  18  X  42  _ 

the  coiler  per  minute]  "  ^^"  ^  l6~x"Wx  69  ~ 

The     revolutions    ofl   _  22  x  18  x  18  X  10  x   20 

the  can  per  minute  J   ""  ^'-"^  ^  46  X  20  X  34  X  36  X  104  ~ 

Whenever  draw  frames  are  changed  from  heavy  slivers, 
to  the  other  extreme,  the  coils  are  frequently  ill-spaced  in  the 
can,  and  vice  versa.  This  may  be  remedied  by  remembering 
that  heavy  sliver  requires  more  space,  and  hence  higher  speeds 
of  the  can  than  light  fine  slivers. 

When  the  sliver  is  coiled  too  widespread  it  is  liable  to  be 
troublesome  through  too  much  tension  caused  by  binding  in  the 
can.      This  may  be  overcome  by  slightly  increasing  the  rate 


106 


COTTON  SPINNING  CALCULATIONS 


of  the  coiler.  On  the  other  hand,  when  the  sliver  is  not  fully 
distributed — indicated  by  a  wide  space  between  it  and  the  can 
side — the  cans  cannot  contain  as  much  as  desirable.  This  may 
be  overcome  by  slightly  reducing  the  rate  of  the  coiler.  When 
the  unoccupied  space  in  the  centre  of  the  can  is  greater  than 
desired,  it  is  due  to  the  can  being  "too  eccentric"  with  the 
coiler.  By  reducing  this,  and  at  the  same  time  the  rate  of  the 
coiler,  this  objection  may  be  removed. 

The  quantity  of  the  production  in  draw  frames  varies  accord- 
ing to  the  speed,  the  system,  and  the  efficiency  of  the  workers. 
In  some  mills,  as  high  as  90  per  cent,  of  the  production,  calcu- 
lated from  the  actual  speeds,  are  obtained  with  slivers  as  high 
as  70  grains  per  yard. 

The  above  may  be  considered  practicable  under  the  best  con- 
ditions. This  would  give  the  following,  per  delivery,  in  a  week 
of  55^  hours : — 


Revolutions  of  front 
roller. 

Weight  of  sliver  in 
grains  per  yard. 

Hanks  per  delivery. 

Pounds  per  delivery. 

320 

55 

50 
55 
60 
65 

70 

13719 

55 
55 

823 

905 

987 

1070 

1152 

Productions  for  Speeds  ranging  from  320  vv  to  380  Eevolutions  pee  Minute 
OF  13-iNCQ  Front  Roller. 


Revolutions  of  front 

Weight  of  sliver  in 

Production  in  pounds  per 

roller  per  minute. 

grains  per  yard. 

week. 

320 

70 

1152 

330 

1198 

3-10 

1234 

350 

1270 

360 

1306 

370 

1337 

380 

» 

1366 

In  medium  fine  (50''-80*)  counts,  the  former  of  the  above 
speeds  and  productions  would  be  considered  ample,  and  the  sliver 
would  range  from  50  grains  per  yard  downwards,  according  to 


AND   COSTS   OF  YARN 


107 


quality  of  the  yarn  and  the  quantity  of  preparation  machinery 
available. 


Revolutions  of  front 

Weight  of  sliver  in 

Production  in  pounds  per 

roller  per  minute. 

grains  per  yard. 

week  per  delivery. 

320 

50-0 

823 

» 

47-5 

783 

» 

450 

744 

42-5 

704 

400 

765 

37-5 

726 

»> 

360 

687 

In  fine  counts,  80^  upwards,  the  speeds  would  range  from 
280  downwards,  and  the  rollers  would  be  1^  inches  in  diameter 
in  three  positions  instead  of  If  inches,  and  the  slivers  down  to 
24  grains  per  yard.     The  productions  are — 


Revolutions  of  front 
roller  per  minute. 

AVeight  of  sliver  In          Production  in  pounds  per 
grains  per  yard.                  week  per  delivery. 

280  X  1^  F.E. 

360 
330 
300 

27-0 
240 

658 
603 
548 
493 
438 

Calculations  relating  to  the  Drafts  in  the  Rollers  (Fig.  21,  Y). 
Between — 
First  and  second  =  7^ ^.  =1-2 


Second  and  third  = 


30  X  24 

24  X  30  X  80  X  100  x  20  x  30  x  9 
36  X  24  X  60  X  20  X  47  X  38  X  10 


=  1-68 


Third  and  fourth  =  !^  ^  !!  ^  ^?  =  3*30 


30  X  20  X   9 


„.    ,       ,  .      ,,         80  X  100 

First  and  fourth   =  ,^  _  —  ^^ 

60  X   20 


6-6 


First  and  third     =  77 


80  X  100  X  20  X  30  X   9 


60  X   20   X  47  X  38  X  10 


=  2-01 


108  COTTON   SPINXIXG  CALCULATIONS 

Xotcs  in  respect  of  this  System  of  Gearing  Rollers. 

(a)  That,  since  P  is  the  customary  change  wheel  for  varying 
the  total  extent  of  the  attenuation  and  the  weight  unit  of  the 
sliver  produced,  any  alteration  of  P  or  of  the  back  roller  wheel 
disturbs  the  draft  between  rollers  2  and  3  only,  and  if  the  total 
draft  be  altered  by  this  means  gradually  to  3'968,  that  between 
2  and  3  would  be  gradually  diminished,  no  attenuation  would 
then  take  place  between  those  rollers,  and  if  altered  to  less 
than  that  amount  contraction  instead  of  attenuation  of  the 
sliver  must  result  between  those  points. 

(h)  The  draft  between  the  rollers  3  and  4  would,  under  the 
circumstances  mentioned  in  paragraph  (a),  always  be  constant, 
and  hence  should  the  wheels  be  altered  to  exercise  a  greater 
draft  than  6'6,  the  draft  between  the  second  and  third  rollers 
only  would  be  increased.  Thus,  in  case  the  total  draft  was 
raised  to  11'9,  the  draft  between  the  second  and  third  rollers 
would  then  become  as  much  as  that  between  the  third  and 
fourth. 

By  this  system  of  gearing  the  variable  draft  is  placed  at  a 
point  which  is  not  the  best.  This  also  may  be  said  of  system  X 
(Fig.  21),  with  this  addition,  that  there  is  room  for  error  in  calcu- 
lation by  overlooking  that  the  two  trains — eight  wheels — are 
involved  in  the  calculation  of  the  total  draft.  Another  feature 
in  these  systems  of  gearing  (Y  and  X)  is  the  backlash  due  to 
the  increased  number  of  wheels  and  indirectness  of  the  gear. 
This  is  best  understood  when  the  effects  upon  the  sliver  are 
considered  with  the  wheels  loosely  geared  or  worn.  On  refer- 
ence to  the  gearing  it  will  be  seen  that  3  will  start  after  4,  and 
2  considerably  after  this,  because  in  the  former  there  are  only 
three  or  four  wheels  against  eight  in  the  latter. 

The  system  of  driving  the  (2)  and  (3)  rollers  direct  from  the 
back  roller  as  shown  in  the  other  figure  has  many  advantages 
over  X  and  Y.  It  ensures  the  variable  draft  between  those 
rollers  having  the  lightest  work  to  perform,  greater  facilities  for 
changes  and  calculations ;  occupies  less  space,  simplifies  the 
parts,  fewer  wheels  are  required,  and  permits  the  use  of  larger 
wheels. 


AND   COSTS   OF  YARN  109 

Exercises. — Calculate  the  drafts  in  Fig.  21  between — 

(a)  1  and  2,  2  and  3, 3  and  4, 1  and  3, 1  and  4,  2  and  4,  when  tlie  compound 
wheel  between  1  and  2  is  20  and  30. 

(b)  1  and  2  when  the  wheel  marked  20  is  21,  22,  23,  and  24  respectively. 

(c)  1  and  4  when  the  wheel  marked  20  is  21,  22,  23,  and  24  respectively. 

(d)  1  and  4  when  P  is  the  inclusive  sizes  from  40  to  60. 

(e)  2  and  3  when  P  is  the  inclusive  sizes  from  40  to  60. 
(/)  1  and  4  when  the  60  on  the  roller  2  is  40,  50,  70,  80. 

(g)  What  should  be  the  weight,  in  grains  per  yard,  and  count  of  the  sliver 
delivered,  in  each  of  the  three  types  of  gearing  given,  if  the  number  of  slivers 
fed  per  delivery  were  in  each  case  six,  and  each  of  these  weighed  at  the  rate  of 
48  grains  per  yard  ? 

(Ji)  If  the  sliver  delivered  by  a  machine,  geared  as  in  Fig.  21,  weighed  54 
grains  per  yard,  what  should  it  weigh  if  the  wheel  P  was  successively  40,  45, 
50,  and  55  respectively  ? 

(i)  What  would  be  the  production  in  pounds  per  delivery  per  week  with  P 
40,  45,  50,  and  55  respectively,  if  with  a  60,  P,  1152  lbs.  were  produced? 

The  Arrangement  of  the  Drafts  in  the  Several  Heads  consti- 
tuting the  Draw  Frame. — The  condition  which  should  govern  the 
extent  of  the  total  drafts  allotted  to  each  head  is  that  each 
should  be  so  rated  as  to  be  continuously  working  without  pro- 
ducing more  or  less  than  is  required  by  the  succeeding  machine. 

It  is  the  most  common  practice  to  have  the  same  number 
of  deliveries  in  each  head,  and  also  for  the  front  rollers  in  these 
to  revolve  at  the  same  rate.  Practice  has  proved  this  most 
expedient.  To  get  the  best  results  under  such  conditions, 
arrange  the  drafts  so  that  the  condition  contained  in  the  last 
paragraph  may  be  realized. 

The  variations  in  the  contents  of  the  cans  from  the  cards 
occasion  considerably  more  loss  of  time  in  the  first  head,  through 
stoppages,  taking  this  at  10,  7,  and  7  per  cent,  respectively  in 
the  three  heads,  and  the  revolutions  of  the  front  roller  at  320 
per  minute  and  If  inches  in  diameter,  the  card  sliver  at  36 
grains  per  yard,  and  that  at  the  last  head  at,  say,  60  grains 
per  yard.  Then  the  productive  capacity  of  the  third  head  would 
amount  to — 

55  hrs.  X  60  X  320  X  If"     22     60      93       ..^^^  „  ,,. 
36^<7000 ^  y  ^  T  "^  100  =  ^^^^  ^^''  ^'''  ^'^'''''^ 

Hence,  the  front  roller  in  the  second  head  would  require  to 
produce  sliver  at  the  same  rate  per  yard,  whilst  that  delivered 


110  COTTON   SPINNING  CALCULATIONS 

by  the  first  head  would  require  to  be  heavier  to  the  extent  of  the 
difference  in  the  loss  of  time,  and  therefore — 

60  X  93      ^^        .  T 

— ^r —  =  62  grams  per  yard 

The  draft  in  the  respective  heads  on  the  assumption  that 
the  doublings  are  6,  in  each  case  must  therefore  be 
In  the  first  head — 

36  X  6 


draft 


=  63 


91  fi 

draft  =  ~  =  3-43 


And  in  the  second  head — 

62  X  6 

draft 


=  60 


•.  draft  =  ?^  =  6-2 
dO 


And  in  the  third  head — 

60  X  6 
draft 


=  60 


/.  draft  =  -TTTT  =  6 
oU 

Fly  Frames. 

The  primary  object  in  fly  frames— slubber,  intermediate, 
rover,  and  jack — is  to  attenuate  the  sliver  obtained  from  the 
drawing  frame  to  the  extent  necessary  to  prepare  it  for  the 
spinning  machine. 

It  would  be  possible  to  dispense  with  fly  frames  if  drawing 
rollers  were  perfectly  adapted  for  attenuating  cotton.  Drawing 
rollers,  as  at  present  constructed,  cannot  attenuate  perfectly 
bodies  of  fibres  varying  in  length.  Cotton  cannot  be  obtained 
which  does  not  vary  in  the  length  of  its  fibres.  In  consequence, 
the  relative  sequence  of  the  fibres  is  altered  during  attenuation 
in  a  degree  proportionate  to  those  variations  and  the  extent  of 
the  attenuation  attempted.  This  means,  that  a  sliver  or  rove 
with    its   fibres   uniformly   distributed   would    have   its   fibres 


AXD   COSTS   OF  YAKN  111 

otherwise  arranged.  The  less  the  variation  in  the  length  of  the 
fibres  the  greater  the  draft  practicable. 

Eepetition  of  these  processes  is  necessitated  to  admit  of 
doubling  and  thereby  absorption  of  the  irregularities  referred 
to.  There  is  no  doubt  that  doubling  of  more  than  two  ends 
would  be  advantageous.  The  difficulties  connected  with  pre- 
senting more  than  that  number  are  the  most  likely  reason  of  its 
not  being  adopted. 

The  Object  of  Twisting. — Twisting  assists  cohesion,  and  is 
employed  to  the  extent  sufficient  to  protect  the  bodies  of  fibres 
at  these  stages. 

The  Direction  of  Twist  and  the  Range  of  Usefulness  of  Twist, — 
The  rule  in  respect  of  the  direction  of  the  twist,  in  rove,  is 

<-  twist :  although  there  are  instances  of  ->  weft  twisting. 
I  I 

The  direction  of  the  twist  has  a  slight  influence  on  the  spin- 
ning :  a  twist  rove  makes  better  and  stronger  yarn  when  it  is 
twisted  finally  in  the  same  direction  than  when  this  is  done 
reversely.  It  is  undoubtedly  the  case  that  roving  twisted  in 
the  same  direction  as  the  ultimate  yarn,  would  secure  better 
results  in  spinning.  The  only  reason  which  can  be  given 
for  this  not  being  practised,  in  respect  of  weft  and  "  reverse  " 
yarns,  is  that  it  may  not  be  so  convenient  to  produce  on  account 
of  necessitating  the  use  of  the  left  hand  in  piecing.  It  is  advan- 
tageous, in  preparing  roving  for  twist  yarn  in  ring  frames,  to 
use  the  maximum,  and  for  weft  or  reverse  yarn  the  minimum 
twist,  constants.  Twist  has  a  beneficial  influence,  when  it  is  in 
the  same  direction  as  that  required  in  the  yarn,  and  when  not 
used  to  excess.  The  reason  for  many  carders  preferring  the 
minimum  twist  is  because  it  enables  a  greater  production,  from 
their  point  of  view,  but  this  is  not  the  case  with  the  spinner. 
Eoving  may  contain  too  little  twist  without  breaking  in  the 
creel.  Care  should  always  be  exercised  to  avoid  twisting  to  the 
extent  which  may  bind  the  fibres  in  excess,  causing  them  to 
withstand  the  subsequent  attenuating  powers. 

Twist  Constants. — The  efficacy  of  twist  varies  in  the  various 
grades  and  kinds  of  cotton  ;  it  is  also  influenced  by  the  degree 


112  COTTON   SPINNING   CALCULATIONS 

of  uniformity  of  the  length  of  the  fibres  and  touch  of  the  cotton. 
The  amount  of  the  twist  per  inch  necessary  to  bind  the  fibres 
to  the  proper  extent  varies  from  \/count  X  0*8  to  \/count  X  1'5. 
Cottons  which  are  long  and  harsh  and  lie  compactly  require 
least,  whilst  those  which  are  short  and  do  not  lie  compactly 
require  most,  twist. 

The  following  is  a  table  of  the  normal  twist  constants. 
These,  when  multiplied  by  the  \/counts  of  the  actual  rove,  will 
give  the  twist  per  inch  suitable  under  most  conditions. 


Slubber. 

from :  0-8 
to :         1-0 

from:  I'O 
to:  1-2 
from:     1*1 


Inter. 

Rover. 

0-9 

0-9 

M 

1-2 

1-1 

1-2 

1-25 

1-3 

1-2 

1-4 

1-4 

1-5 

Sea  Island  and  Egyptian  cottons  .  .  < 
Brazilian,  American,  and  similar  cottons  < 
Indian  and  similar  cot'. ons     .     .     .     .     -j  ,    .         ...^ 

The  Gearing  in  Fly  Frames  (Fig.  22). — The  gearing  in  fly 
frames  is  identical  in  all  the  principal  makes.  It  consists  of 
a  principal  shaft  called  the  frame  shaft,  and  from  this  all  the 
parts  receive  their  motion. 

(a)  The  Rollers. — The  front  roller  is  connected  with  the  frame 
shaft  referred  to  by  means  of  a  train  consisting  of  four  or  five 
wheels,  F,  E,  D,  C,  B,  named,  respectively :  the  twist,  the  twist 
carrier  or  compound,  the  top  cone,  the  end  of  top  cone,  and  the 
end  of  the  front  roller  w^heels ;  a  compound  wheel  instead  of  E 
being  necessary  when  considerable  range  of  twist  are  necessary. 
The  back  and  middle  rollers  are  connected  with  the  front  in  the 
following  manner :  a  train  of  four  wheels,  28,  90,  40,  56,  and 
named  respectively  the  front  roller  (F.E.W.),  the  crown  (C.W.), 
the  pinion  (P.W.),  and  the  back  roller  wheels  (B.R.W.) ;  these 
comprise  the  connection  to  the  latter  roller,  the  crown  and 
pinion  being  compounded.  The  middle  roller  is  connected  with 
the  back  through  the  medium  of  three  wheels,  25,  C,  18 ;  they  are 
named  the  back  roller  (driver),  carrier,  and  middle  roller  wheels. 

(h)  The  Spindles. — The  shafts  driving  these,  one  only  is  shown, 
are  connected  by  a  train  of  three  wheels,  33,  H,  33,  in  case  of 
the  back  line  of  spindles ;  and  a  fourth  wheel  on  the  front  shaft 
gears  with  that  on  the  shaft  driving  the  back  line  of  spindles. 


AND  COSTS   OF  YARN 


113 


These  spindle  shafts  are  furnished  with  skew  bevels,  60,  and 
these  drive  the  bevels,  21,  on  the  spindles.  The  value  of  this 
train  is  fixed. 

(c)  Winding. — The  Bobbins  are  driven  from  two  points  upon 
the  frame  shaft,  T.W.  and  M,  the  motion  from  these  two  points 
being  brought  together  at  the  terminal  wheel,  14,  in  the  differ- 
ential. The  bobbin  driving  shaft  (O)  is  connected  with  the 
sleeve  wheel  of  the  differential  N,  by  means  of  four  or  five  wheels 


V'dia. 


/       I 

1         Top  Con 


-nl 


one      t- 


f pitch    60^^ 

Ratchet  Wheel 


Bottom  C 


Fig.  22. 

in  case  of  the  front,  and  three  or  four,  45,  C,  40,  in  case  of  the 
back  bobbin  shaft.  These  wheels  are  known  as  the  swing 
train.  The  sleeve  N  acquires  its  motion  from  the  two  points, 
receiving  a  fixed  contribution  from  one,  M ;  and  a  variable  con- 
.tribution  from  A,  the  other  of  these  two  points  ;  the  fixed  portion 
here  referred  to  being  contributed  by  that  part  of  the  differential 
which  is  fixed  to  the  jack  shaft.  In  some  cases  that  part  is  a 
wheel.  The  variable  contribution  is  received  by  the  differential 
from  the  twist  wheel,  T.W.,  on  the  frame  shaft,  the  motion 
passing  through  the  top  and  bottom  cones,  and  thence  through  a 


114  COTTON  SPINNING  CALCULATIONS 

train  consisting  of  a  varying  number  of  wheels,  numbered  on  the 
figure  36,  36,  46,  50,  46, 106.  The  fixed  contributor  is  arranged 
to  supply  the  movement  necessary  to  rotate  the  bobbins  at  the 
same  rate  as  the  spindle ;  the  variable  contributor  communi- 
cating only  that  necessary  to  obtain  winding  at  the  desired 
tension.  By  this  arrangement,  the  cones  completely  control 
the  winding.  When  they  cease  to  contribute,  winding  ceases, 
through  the  bobbins  then  assuming  the  rate  of  the  spindles.  The 
wheels  in  this  latter  connection  are  known  by  the  following 
names :  the  bottom  cone,  change  shaft,  winding  shaft,  differ- 
ential, differential  sleeve,  swing,  bobbin  shaft,  skew  bevels,  and 
bobbin  wheels. 

The  Consequences  of  altering  the  Value  of  the  Cone  Train. — The 
value  of  the  wheel  train,  connecting  the  fixed  contributor  with 
the  bobbins,  should  be  a  constant,  and  therefore  any  departure 
from  the  above-named  conditions  will  result  in  imperfect  wind- 
ing. The  value  of  the  wheel  train  connecting  the  twist  wheel 
with  the  differential  should  likewise  be  constant.  The  value 
of  the  belt  connection  on  the  two  cones  is  the  medium  for  pro- 
viding the  acceleration  or  retardation  of  the  bobbin  necessary 
to  obtain  the  proper  winding  tension  ;  this  being  a  plus  or  minus 
contributor  according  to  the  conditions  of  winding  adopted.  The 
two  conditions  in  respect  of  winding,  referred  to,  are  bobbin  lead 
and  flyer  lead.  In  the  former  of  these  the  winding  is  occasioned 
by  the  excess  in  the  rotation  of  the  bobbin  over  that  of  the  flyer  ; 
and  vice  versa  in  flyer  lead.  In  flyer  lead  the  bobbin  must 
be  accelerated  to  the  extent  coincident  with  the  proportional 
change  in  the  size  of  the  bobbin  at  the  commencement  of  each 
new  layer  of  coils,  but  only  in  respect  of  that  portion  of  their 
motion  supplied  through  the  medium  of  the  cones.  In  bobbin 
lead  retardation  takes  the  place  of  acceleration.  The  connection 
of  the  front  roller  with  the  bobbins  is,  therefore,  such  that  the 
latter  creates  a  winding  rate  coinciding  with  the  rate  of  delivery 
by  former.  Any  change  in  the  rate  of  rotation  of  the  front 
roller  obtains  a  corresponding  change  in  the  winding  rate. 

The  cone  drums  are  constructed  to  comply  with  the  require- 
ments of  certain  sizes  of  bobbins,  each  portion  being  adapted 
for  a  certain  size,  and  that  only.     Altering  the  value  of  this 


AND  COSTS   OF   YARN 


115 


train  of  wheels  is  most  likely  to  place  the  cone  strap  on  a  wrong 
part  of  the  cones.  There  is  only  one  part  that  will  give  the 
fractional  change  of  speed  corresponding  with  the  fractional 
increase  that  each  added  layer  bears  to  the  size  of  the  surface 
it  is  laid  upon.  If  the  strap  is  not  on  that  portion  of  the  cones, 
then  the  tension  of  winding  will  be  inaccurate. 

((?)  The  Spacing  of  the  Coils. — This  is  obtained  by  the  move- 
ment of  the  bobbin,  vertically,  past  the  guiding  point  of  the 
flyer.  This  raising  and  lowering  movement  of  the  bobbin  is 
derived  also  from  the  twist  wheel,  through  the  cones,  by  a  con- 
necting train  intercepting  the  train  between  the  bottom  cone  and 
the  differential  connections,  namely,  13,  60,  (W),  10,  100,  (V), 
14,  56,  (U),  36,  50,  (T),  14,  90,  (S),  22.  The  necessity  for  this 
vertical  movement  being  derived  from  the  cones  arises  through 
the  number  of  coils  wound  retarding  at  a  rate  inverse  to  the 
increasing  size  of  the  bobbin.  The  number  of  wheels  employed 
in  this  connection  vary  somewhat.  The  reversion  in  the  direc- 
tion of  the  vertical  movement  is  obtained  by  means  of  E.B.,  the 
reversing  bevels ;  these  alternately  engage  their  driving  bevel. 

The  wheels  in  this  connection  are  known  by  the  following 
names :  Top  change,  top  of  upright,  strike  bevel,  reversing 
bevels,  reversing  bevels  shaft,  cannon  shaft,  bottom  change 
shaft,  lifting  shaft  wheels,  and  lifting  racks. 


Speeds  of  the  Parts  in  Fly  Frames. 


Subject. 

Details  of  calculation  (Fig.  22). 

Revolu- 
tions per 
minute. 

Surface  rate  in 

inches  per 

minute. 

Front  roller,  B 

Spindles,  P  .     . 
Twist  per  inch 
Twist  constant 

350  X  39  X  35 

35  X  130  ~ 
105  X  1"  X  22 

7  ~ 
350  X  33  X  60  _ 
33  X  21 
revolutions  of  spindle  per  minute 
inches  del.  by  the  F.R.  per  minute 

-  330"  -  ^  "^ 
twist  per  inch 

V count 
Note. — Count  suitable  deiJends  upon  the 
twist  constant  used. 

105 
1000 

330" 

116 


COTTON   SPINNING   CALCULATIONS 


Subject. 


Top  coue  (0,  D) 
Bottom  cone,  Y 


Details  of  calculation  (Fig.  22). 


Draft  between"! 
the  back  and I 
front  rollers  [ 
(1st  and  3rd)  j 

Bobbin  lifting\ 
shaft,  S       / 


Bobbin    .     .     . 


350  X  39  _ 
35  ~ 
Assuming  the  strap  on  the  parts  G"  top 
cone  and  o\"  bottom  cone — 

350  X  3)  X  6  _ 

35  X  3i  ~ 

Assuming   the  strap  on  the  parts   3J" 

diameter   top   cone  and   G"  diameter 

bottom  cone — 

350  X  39  X  31  _ 

35  X  G  ~ 
56x90  X  r_  ,.g 
40  X  28  X  1"~ 

350  X  39  X  6  X  36  X  13  X   10  X  14 
35  X  3i  X  36  X  60  X  lOOx  56 

36  X  14  _ 

^  50  X  90  ~ 

Note. — The  above  is  when  cone  strap  is 

assumed  in  positions  6"  in  diameter 

driver  cone  and  3J"  in  diameter  driven 

cone. 

And  when   cone   strap   is  in  positions, 

rcspectivclv,  SJ",  6" — 
350  X  39  X  3J  X  36_X  13  x    10  x  14 
35x  6  X  36  X  GO  X  100  x  56 

36  X  14  _ 

^  50  X  90  ~ 

To  wind  without  stretching,  assuming 

the   winding  circle 

and  bobbin  lead — 


1|"  in   diameter 
330 


If  flyer  lead — 


li  X 


+  1000  = 


1000  -  -, 


330 


n  X  f  - 

Maximum  size  of  bobbin  that  the  cones 
are  adapted  for  — 

-Its,    ^X6    _  4-25" 

When  the  bobbin  is  the  maximum  bize, 
4J",  and  bobbin  lead — 

If  flyer  lead — 

For  calculations  of  the   speeds  of  the 
bobbins  as  per  gearing,  see  p.  127. 


Revolu- 
tions per 
minute. 


390 


720 


211-2 
Kaiio 

1 :4-5 


0-437 


Surface  rate  in 

incliea  per 

minute. 


0-128 


1084 


916 


1024-7 


975-3 


0-88 


330"  in  excess 

of  flyer  pres- 

ser 
330"      slower 

than       flyer 

pressure 


AND  COSTS   OF  YARN  117 

The  Change  Wheels  in  the  afore-mentioned  Trains  respectively.— 
The  following  are  the  customary  change  wheels  :— 

(a)  For  altering  the  rate  of  the  rollers  relative  to  the  spindles 
and  thereby  the  twist— twist,  compound,  and  top  cone  shaft 
wheels,  in  the  order  named. 

For  altering  the  total  draft  or  the  attenuating  powers  of  the 
rollers— pinion,  back  roller,  crown,  and  front  roller  wheels. 

For  altering  the  drafts  between  the  individual  rollers,  the 
small  wheels  on  the  back  or  middle  roller. 

(b)  None  of  the  wheels  in  this  train  are  altered. 

(c)  For  altering  the  tension  of  winding.  This  should  be 
done  by  the  ratchet  wheel  or  adjusting  the  position  of  the  cone 
strap  forks.  The  practice  of  changing  one  of  the  wheels  in  this 
train,  connecting  the  differential,  which  is  generally  recognized, 
is  open  to  serious  objections,  which  are  stated  in  the  section 
dealing  with  winding,  p.  127. 

00  For  controlling  the  spacing  of  the  rove  upon  the  bobbin. 
The  lifter  change  shaft  wheel  and  strike  bevel  are  the  usual 
change  points. 

Alterations  in  the  Draft.— Alterations  in  the  draft  are  neces- 
sary when  the  count,  or  the  weight  per  unit  of  length,  are  not 
as  desired.  Also,  when  a  change  is  made  in  the  feed,  and  a 
corresponding  change  in  the  delivery  is  not  required. 

The  formula  when  changing  the  draft  or  the  counts,  is— 

Present  draft  X  count  desired  ,^   count  of  present  feed  _i    draft 
present  count  count  of  distended  feed~|i-equired 

When  the  weight  takes  the  place  of  the  count,  it  is  necessary 
to  bear  in  mind  that  the  weight  is  inverse  to  the  count,  and  that 
this  necessitates  the  inversion  of  the  two  terms,  desired  and 
present,  in  the  above  equation. 

The  total  roller  draft  may  be  altered  by  changing  the  size  of 
any  of  the  four  wheels  in  the  train  connecting  the  back  with  the 
front  roller.  The  pinion  wheel  is  the  recognized  change  wheel, 
and  the  back  roller  wheel  is  changed  when  the  limits  in  respect 
of  the  former  have  been  reached.  When  the  limits  of  the  two 
former  are  exhausted  the  crown  wheel  is  changed,  but  this  is 
not  often  necessary. 


118  COTTON   SPINNING  CALCULATIONS 

Changes  in  the  count  delivered  may  be  made  by  varying 
the  count  of  the  feed  or  the  draft  in  the  direct  proportion. 

Changes  in  the  count  fed  may  be  checked  by  inverse  changes 
in  the  draft. 

Changes  in  the  sizes  of  the  drivers,  in  the  draft  train  of 
wheels,  obtain  inverse  changes  in  the  draft  and  count,  and 
direct  changes  in  the  weight  per  unit  of  length. 

Changes  in  the  sizes  of  driven  wheels  in  the  draft  train  have 
the  inverse  effect  to  the  drivers. 

Alterations  in  the  Draft,  how  made. — Changes  in  the  draft,  or 
in  the  count  produced,  do  not  affect  the  extent  of  the  length 
delivered  by  the  front  roller.  Such  changes  always  affect  the 
weight  of  the  delivery,  per  unit  of  length,  in  inverse  terms. 

The  draft,  as  contained  in  the  present  roller  gearing  (Fig.  22), 

is  as  follows  : — 

25  X  — 

Between  the  first  and  second  rollers  =  -=-^ A  =  1*21 6 

18  X  1" 

,       ,,,.  ,  18  X  56  X  90  X  I       ^„. 

second  and  thn-d    „      =  25  x  40  x  28  X  r  =  ^  ^^ 

„    ,       ,  ,,  .   ,  56x90  X  1"       ... 

„  first  and  third         „      =  40^28 "xl.^'  "" 

Any  change  in  those  wheels  would  have  effects  correspond- 
ing with  those  noted  in  respect  of  the  rollers  in  drawing 
frames. 

The  count  obtained  by  the  above  attenuation  in  the  rollers 
would  be  4*5  times  finer  than  the  feed. 

The  feed  in  the  slubber  generally  consists  of  one  end  per 
rove  delivered,  whilst  in  the  intermediate,  rover,  and  jack  it 
always  comprises  two  ends.  Thus,  in  the  case  where  0*2  is  the 
count  of  the  feed  in  a  slubber  having  4*5  of  a  draft,  0*2  x  4-5 
=  0"9  would  be  the  count   delivered.      An  intermediate  with 

0*9 

4'5  draft,  treating  slubbing  of  0*9  count,  would  produce  -„-  ^  ^'5 

=  2025  count.     A  roving  frame,  with  a  like  draft,  using  that 

2*025 
count  of  intermediate  rove,  would  produce  — ^ —  X  4*5  =  4*556 

count. 


AND   COSTS   OF   YARN 


119 


A  change  in  any  of  the  wheels  connecting  the  first  or  back 
with  the  front  roller  would  have  the  following  effect : — 

If  a  driver,  the  count  and  the  draft  would  be  altered  in  the 
inverse,  and  the  weight  in  the  direct  proportion. 

If  a  driven,  the  count  and  the  draft  would  be  altered  in  the 
direct,  and  the  weight  in  the  inverse  proportion. 

Altering  the  Draft. — The  following  would  be  the  draft  and 
count  with  the  draft  wheels,  as  stated  below,  when  the  other 
roller  gear  is  as  given  in  Fig.  22 ;  the  count  of  the  rove  fed 
beinor  2-025. 


If  the  pinion  was  altered  to     60 

50 

45 

36 

30 

Tlie  draft  would  become       3-0 

3-6 

4-0 

5-0 

6-0 

The  count  would  become      3-03 

3-64 

4-05 

5-05 

6-06 

If  the  back-roller  wheel  was  altered  to 

51         48 

42 

60         65 

70 

The  draft  would  become 

4-1       3-86 

3-37 

4-82      5-22 

5-62 

If  the  front  roller  wheel  was  altered  to 

26 

24 

22 

20 

The  draft  would  become 

4-85 

5-25 

5-73 

6-3 

If  the  crown  wheel  was  altered  to   130 

120 

110 

100         80 

70 

The  draft  would  become                  6-5 

6-0 

5-5 

5            4 

3-5 

Note. — The  front  roller  and  pinion  wheels  (28  and  56)  are  drivers. 
The  crown  and  back  roller  wheels  (90  and  56)  are  driven. 
The  ratio  of  the  crown  to  the  front  roller  wheel. 
The  ratio  of  the  pinion  to  the  back  roller  wheel. 

That  any  pairs  of  these  wheels  possessing  these  ratios  will  produce  the  same 
results. 

Examples  and  Exercises  in  Changikg  the  Draft. 


1  2 

2  ? 

3  2 


"Bo-i: 


Draft. 

? 

6 

5-5 

Draft  gear.    Diameters  of  F.R. 
and  Back  R.  alike. 

F.R.W. 

C.W. 

P.W. 

B.R.W. 

25 

25 
25 

100 
100 
100 

? 
40 

? 

50 
60 

.T.    1.      ,      T^    rx      5x2      ^       50        100      _ 
A^  orking  1.— Draft  -  —^  =  ^ ."  p^  X  ,^^-  =  5 


Working  2. — Count  fed  = 


50^ 
W 

5X2 


5        2j 


,„    B.R.W.      100      „ 


...B.R.W.  =  i^-^^^^  =  60 


120 


COTTON  SPINNING  CALCULATIONS 


^v     T        o       n        .IV  1        2        .  .        -  -     CO  X  100        .  _ 

>\  orkinsr  3. — Count  aelivered  =  -  x  oo  =  5o;  — r ^--  =  o'5 

°  2  ?  X  2o 

.p.W.  =  ^^^?  =  43-6 
55  X  2o 


9 
10 
11 
12 


5J  c  rti  "^^ 


.Q  S 

0} 


"  c  *- 

'tc  =  >       Draft. 


2-775 


30  yds.  = 
125  prrs. 


30  yds.  = 

125  grs. 

30  yds.  = 

135  grs. 

30  yds.  = 

125  grs. 

30  yds.  = 

135  grs. 

0-18 

0-17 

? 

0-2 


to  =  > 


I     ? 

6-0  I 

Ditto  I 

G-0  1 

30  yds.  = 

50  grs. 

5-2  I 

50  ! 


^^ 

6 

" 

5 

u 

G 

»1 

G 

1 

? 

1 

? 

1 

0-7G5 

1 

0-96 

Draft  gear.    Diameters  of  F.R. 
and  Back  R  a  ike. 


F.E.W.    C.W.       P.AV.     B.R.W 


28 
28 


28 

28 

25 
25 
25 

25 


90 
90 


28 

90 

28 

90 

„ 

5» 

» 

» 

90 

90 

100 

? 
100 
100 


40 


50 


40     i  56 

40     I  T 

Eatio  ? 

40     [  56 

Eatio  ? 


56 
56 


60 

CO 

?  ? 

50  I  60 

56  '.  63 

50  1  ? 


j  Change  to  the  latter 
'  of  these  conrU- 
!     tions. 

From  these  condi- 
tions change  to 
the  latter. 

From  these  condi- 
tions change  to 
the  latter. 


The  following  must  always  be  known  to  enable  the  gearing 
to  be  adapted  for  the  production  of  any  specific  count : — 

(1)  The  count  required. 

(2)  The  count  of  the  feed. 

(3)  The  characteristics  of  the  cotton. 
(1)  and  (2)  determine  the  draft. 

(1)  and  (3)  determine  the  twist. 

The  Eate  of  the  Winding  and  Spacing  of  the  Coils  cannot  be 
accurately  ascertained  by  calculation  on  account  of  the  dissimi- 
larity in  the  size  of  rovings.  The  winding  must  be  regulated 
by  adjusting  the  position  of  the  strap  on  the  cones.  The  rate 
of  the  vertical  movement  of  the  bobbin  rail  must  be  adjusted 
to  space  the  coils  without  tendency  to  override  or  apertures 
Generally  about  six  coils  of  count  one  can  be  laid  per  inch 
This  is  useful  as  a  basis  in  the  absence  of  other  data. 


AND   COSTS   OF   YAEX  121 

The  twist  per  inch  obtained  by  the  gearing  as  per  Fig.  22 
=  3-03  inches.  According  to  data  on  p.  112,  the  twisting 
would  be  adapted  for — 

(a)  If  Sea  Islands  cotton  (?^J  =  O'l 

(h)  If  Egyptian  cotton  (^~f  =  9-1  to  G-4 

(c)  If  Brazilian  cotton  f^Y  =  (3.4 

(d)  If  American  cotton  (^-^^2^)'  =  6-4  to  5-4 

(e)  If  Indian  cotton  (^~~^f  =  47  to  41 

Thus  five  frames  employed  as  above  stated  with  the  draft 
4-5 :  the  count  of  the  feed  and  that  in  the  creel  would  be 
respectively — 

9'1 

(«)  475  =  2-02  /.  2-02  X  2  =  404 

C  'A 

^^^  ¥5  "  -^'^'-^  •*•  1"^2  X  2  =  2-84 

p  •  i 
^""^  4^  "  ^'^^  •'•  1-^2  X  2  =  2-84 

5*4 
(d)  --  =  1-2  .-.  1-2x2  =  2-4 

4*7 
(0  4:5  =  104  /.  104  X  2  =  208 

4-1 

°^'  4:5  =  0-91  .-.  0-91  X  2  =  1-82 

A  change  in  the  pinion  wheel  would  have  the  inverse  effect 
upon  the  counts  produced,  and  would  influence  the  weight  per 
unit  of  length  in  the  direct  proportion.  Therefore  a  30-draft 
pinion  instead  of  40  would  produce  the  following  counts,  assum- 
ing the  feed  as  in  the  above  instances  :— 


30 

6-4  X 

40 

30 

6-4  X 

40 

30 

5-4  X 

40 

30 

4-7  X 

40 

122  COTTOX   SPINNING   CALCULATIONS 

(«)  — on— =  12  1 


(c)  "-^3^  =  8-5 

id)  ^^^^  =  7-2 


(.)  ^-  =  6-27 

A  change  in  the  back  roller  wheel  would  have  the  inverse 
effect  to  that  of  the  pinion. 

Whenever  the  count  is  changed,  it  would  become  necessary 
to  re-adjust  the  twist  per  inch  to  \/ count  X  twist  constant. 
The  rate  of  the  front  roller  would  need  altering  in  the  pro- 
portion inverse  to  the  twists.  Thus,  assuming  the  twist  wheel 
in  each  of  the  frames,  referred  to  in  the  last-mentioned  examples, 
39,  the  changes  in  count  would  necessitate  the  following  altera- 
tions in  the  twist  wheel : — 

T.       ,  s    39  X  \/9l 

For  (a) -^ 

Note. — The  twists  are  in  the  direct  proportion  of  the  square  root  of  the 
counts,  and  hence  the  latter  may  substitute  the  former. 


For   (h) 

39  X  \/6-4 

\/8"5 

For  (c) 

39  X  \/¥l 

\/¥5 

For  (d) 

39  X\/r2 

\/5^ 

For   (e) 

39  X  \/4-7 

Assuming  x  the  size  of  the  ratchet  wheel  and  y  that  of  the 
lifter  change  wheel,  the  following  procedure  would  obtain  x  and 


AND   COSTS   OF   YARX  123 

y  adapted  for  the  above-named  changes  :  because  the  size  of 
the  rove  and  yarns  of  a  given  class  are  found  to  vary  inversely 
as  the  square  root  of  their  counts  when  other  conditions  are 
equal. 

For  (a)     \ and  ^-~ 

^  ^    v/9-1  \/l21 

.,.  aj\/8-5        ,  2/\/8-5 

Note.— ic  must  contain  more  teeth,  because  these  wheels  are 
made  a  standard  size  by  each  maker ;  they  differ  in  the  pitch 
of  their  teeth  only. 

«,  controls  the  movement  of  the  cone  strap  at  the  completion 
of  each  layer  on  the  bobbin.  It  is  this  movement  that  obtains 
the  retardation  in  the  speed,  of  the  bottom  cone,  necessary  to 
secure  perfect  tension  in  winding.  The  extent  of  the  movement 
of  the  cone  strap  must  be  in  accordance  with  the  proportional 
increase  resulting  from  each  layer  laid  upon  the  bobbin.  Hence, 
the  number  of  teeth  contained  in  these  wheels  must  be  altered 
relatively,  inverse  to  the  square  root  of  the  counts,  which  sum 
represents  the  thickness  of  the  roves  wound. 

y  must  contain  fewer  teeth  for  smaller  roves  in  the  direct 
proportion  of  their  diameter,  these  are,  for  the  same  kind  of 
cotton,  relatively  inverse  to  the  square  root  of  their  counts  ; 
because  a  smaller  rove  requires  less  space,  and  hence  slower 
speed  of  the  bobbin  rail,  of  which  train  2/  is  a  driver.  If  it  was 
preferable  to  alter  a  driven  wheel  in  that  train,  then  a  wheel 
containing  more,  instead  of  less,  teeth  would  be  necessary. 


Exercises  ik  Miscellaneous  Fly  Frame  Calculations. 

1.  In  a  roving  frame  the  twist  -wheel  has  30  teeth,  and  drives  hy  a  carrier 
the  wheel  in  the  middle  of  the  top  cone  shaft,  containing  40  teeth.  On  the  end 
of  the  latter  shaft  a  48  gears  with  one  on  the  front  roller  containing  130  teeth. 
The  front  roller  is  1^  inches  in  diameter.  The  spindle  bevel  wheel  has  30  teeth, 
and  that  driving  it  has  55  ;  a  wheel  of  40  teeth  on  this  latter  shaft  is  driven  from 
the  frame  shaft  by  one  of  the  same  size.     Find  the  twist  per  inch. 

2.  Ascertain  the  twist  per  inch,  the  twist  constant,  the  production  in  hanks 


124  COTTOX   SPINNING  CALCULATIONS 

and  ounces  per  spindle  per  10  hours,  under  the  following  conditions  in  a  roving 
frame.  Revolutions  per  minute:  spindle,  1150;  F.R.  120:  diameter,  IJ  inch; 
draft,  5,  count  fed  :  two  ends  of  3-5  hank  intermediate  rove ;  loss  of  time, 
8  per  cent. 

3.  A  roving  frame  is  required  to  produce  9-hank  rove  containing  twist  equal 
to  vcount  X  1'4,  and  the  spindles  making  1200  revolutions  per  minute;  the 
diameter  of  the  front  roller  is  1}  inch.     At  what  rate  must  the  roller  be  driven? 

4.  At  what  rate  must  the  bobbins  rotate  to  obtain  good  winding  during  the 
first  layer  under  the  following  conditions  :  Gear  from  the  front  roller  to  the  frame 
shaft,  J-jSii^  11^  that  from  the  frame  shaft  to  the  spindles,  ^,  f]g  ;  diameters,  of 
front  roller,  IJ  inch,  of  the  bobbin,  1|  inch  ;  revolutions  per  minute  of  the  frame 
shaft,  300? 

5.  A  fly  frame  making  a  6-hank  rove  has  the  following  change  wheels : 
Draft  pinion,  42 ;  twist,  36 ;  ratchet,  40 ;  lifter  (driver),  26.  What  sizes  of 
these  wheels  respectively  would  be  required  for  a  5-hank  ? 

Ans.  50,  39,  37,  29. 

6.  The  spindles  in  a  slubber  making  a  0-75-hank  rove  are  observed  to  rotate 
4"5  times  per  1  of  the  front  roller,  which  is  1]  inch  in  diameter  :  the  change 
wheels  are — twist,  40  ;  ratchet,  19  ;  lifter,  26 ;  draft  pinion,  42  :  and  the  spindles 
are  known  to  make  550  revolutions  per  minule.  Ascertain:  («)  the  present 
twist  per  inch  ;  (i)  the  twist  per  inch  suitable  for  0'58-hank,  and  also  the  change 
wheels  required ;  (c)  the  rate  of  production  in  both  cases  in  hanks  and  ounces 
per  spindle  per  10  hours,  assuming  15  per  cent,  represents  the  loss  of  time. 

Ans.  1-15  ;  1-01,  49,  or  |f ,  32,  63  ;  81,  173  ;  9-93,  358. 

7.  What  lifter  wheels  would  be  most  suitable  in  using  the  same  cotton  for 
I'O  and  for  0'5  hank,  if  it  was  known  that  6  coils  per  inch  was  the  most  satis- 
factory spacing  for  1  hank  and  a  28  lifter  wheel  (driver)  gave  7  coils  per 
inch?  Ans.  24;  17. 

8.  What  sizes  of  ratchet  wheels  would  be  most  suitable  in  using  the  same 
cotton  for  1*0  and  for  0'5  hank,  if  it  was  known  that  a  14  was  most  suitable  for 
0-68  hank?  Ans.  17;  12. 

9.  The  spindles  in  a  roving  frame  producing  7-hank  roving  make  1120,  and 
the  front  roller  100,  revolutions  per  minute  ;  the  latter  is  1^  inch  in  diameter. 
What  twist  per  inch  should  the  rove  contain  ?  Give  the  twist  constant  and  the 
hanks  produced  in  10  hours'  uninterrupted  working.  Ans.  3*17  ;  1*2  ;  7'02. 

10.  The  draft  in  the  rollers  of  a  roving  frame  is  6  and  the  intermediate 
roving  is  2*6  hanks,  and  two  of  these  are  doubled :  what  count  of  rove  will  be 
made  ?  If  the  count,  ascertained,  has  to  be  changed  to  6',  and  the  draft  wheels 
and  rollers  are  F.E.W.  20,  C.W.  80,  P.W.  40,  B.E.W.  60;  diameters,  F.R.  IJ 
inch,  B.R.  1^  inch,  which  of  these  wheels  would  you  alter,  and  to  what  extent  ? 

Ans.  7-8— P.W.  to  52. 

11.  A  roving  frame  is  making  7-8  hank-roving  with  the  following  wheels: 
Draft  pinion,  40  ;  twist  wheel,  38  ;  ratchet,  46  ;  lifter,  28,  What  wheels  would 
be  needed  for  6  ?  What  eftect  would  these  changes  have  upon  the  length  and 
weight  produced  ? 

Ans.  52,  43,  40,  32  increase  in  lengtli,  38  to  43 ;  increase  in  weight, 
6  to  8-9. 


AND   COSTS   OF   YARN 


125 


Exer- 

' 

Cottiin  and 
count. 

Twist. 

Roller  gear. 

AVind- 
iiig. 

Spacing 
lifter 
wheel. 

Count 
fed. 

Twist 

cise 
No. 

b. 
S 

OS 

.o 

'a 

J3 

Pi 

1 

1-3 

a-  03 
O  I* 

&  P. 

stant. 

Present 

Required 

Present 

Required 

Present 

Required 

Present 

Required 

Present 

Required 

Present 

Required 

American  0  4 

8 
Egyptian  10 

12 
American  42 

3 
Indian  2§ 
„       2J 
Egyptian  16 

20 
Indian  3 

303 

? 

? 

4-5 

? 
? 

? 

? 

4-8 
p 

? 
? 

39 

■? 
? 
? 
? 
? 

? 
? 
36 

? 

50 

? 

4-5 

? 
5 

? 

? 
? 
? 
? 
5 
? 
? 
5 

45 

? 

9 

? 

? 

? 
? 
? 

60 

? 
50 

? 

56 

? 

? 
? 
? 

9 

56 
56 
60 
60 
54 
54 

40 
? 

52 

? 
33 

? 
20 

? 
56 

9 

24 

9 

14 

? 
14 

17 

? 
? 
? 

18 
? 

56 

? 
42 

? 
56 

56 

48 

? 

42 

? 

2-84 

55 
? 

5 
1-4 

5» 

1-0 

? 

1-4 
»> 

1-28 

I'l 

? 
1-3 

r4 

55 

? 

? 

1-4 
1-5 

Winding  in  Fly  Frames  is  obtained  by  the  Bobbin. — Winding 
in  these  frames  is  clue  to  the  bobbin  rotating  at  a  slower 
or  quicker  rate  than  the  spindles.  In  the  former  case  the 
"  flyer  leads  "  and  in  the  latter  the  "  bobbin  leads."  The  rates 
of  rotation  of  the  spindles  and  rollers  being  constant,  winding  is 
obtained  by  that  of  the  bobbin  differing  from  the  former  of 
these  to  an  extent  sufficient  to  wind  the  amount  delivered  by 
the  rollers.  Generally,  the  range  in  the  size  of  the  bobbins  is 
from  1-^-  inch  upward,  empty,  to  below  6  inches  when  full.  It 
is  not  often  that  full  bobbins  exceed  more  than  four  times 
their  size  when  empty. 

Winding  is  arrested,  in  these  machines,  when  the  bobbins 
assume  the  same  rate  of  rotation  as  the  spindle  or  flyer.  Thus 
if  the  latter  exceeds  the  former,  or  vice  versa,  the  difference 
represents  the  coils  wound.  However  large  the  bobbin  becomes 
— when  winding  is  required — the  rate  of  rotation  must,  as  its 
size  develops,  approach  that  of  the  spindle,  but  never  attain 
the  same  speed  equal  to  it.  Therefore,  if  the  bobbin  leads  and 
the  spindle  makes  1000  revolutions  per  minute,  however  large  the 
bobbin  may  become,  its  rate  must  be  something  more  than  1000. 
In  the  case  of  the  bobbin  being  1^  inches  in  diameter,  empty, 
and  6  inches  diameter  when  full,  and  the  length  wound  equal  to 
120  times  the  circumference  of  the  former  size,  then  the  bobbin 


126 


COTTON  SPINNING  CALCULATIONS 


must  revolve  at  the  rate  of  1000  + 


120  j<  1.^ 
6 


=  1030  revolutions 


when  full,  as  against  1000  +  120  empty. 

The  Use  of  Cone  Drums. — Cone  drums  are  used  to  give  the 
necessary  variations  in  the  speed  of  the  bobbins.  Their  work 
consists  of  contributing  toward  the  driving  of  the  bobbin  an 
amount  sujBicient  only  to  ensure  winding  at  the  desired 
tension,  the  remainder  an  amount  which  is  always  equal  to  the 
rate  of  the  spindle  being  obtained  from  a  fixed  contributor. 

The  Use  of  Differentials. — Differentials  admit  of  the  trans- 
mission of  the  motion  from  the  two  above-named  sources  with 
the  most  satisfactory  results.  A  simple  way  of  calculating  the 
motion  transmitted  through  the  differential  gear  is  as  follows  : — 

Let  n  denote  the  motion  issuing  from  it ;  m,  that  portion 
of  n  derived  from  the  fixed  contributor  ;  a,  that  portion  of 
n  derived  from  the  variable  contributor;  M  and  A,  the  rates 
of  those   parts   of  the   differential    responsible   for  m   and    a 


Fig.  23. 

respectively  ;   t,  the  values  of  the  respective  connecting  trains 
connecting  M  and  A  with  n — 

then  n  consists  of  ??i  ±  a 
Applying  this  to  the  Holdsworth  differential  gear  (Fig.  23)  : — 
When  M  is  at  rest  and  motion  is  imparted  to  A, 

revolutions  oi  n  =  k  ±  Kt  (in  the  same  direction). 


AND   COSTS   OF  YARN  127 

When  A  is  at  rest  and  M  is  moved,  then — 

revolutions  of  w  =  Mt 

in  the  opposite  direction  to  M.  Therefore  when  A  and  M  rotate 
in  the  same  direction, 

revohitions  of  n  =  K  ±  A.t  ~  Mt 

and  when  A  and  M  revolve  in  opposite  directions, 

revolutions  oi  71  =  A  ±  At  +  Mt 

Thus,  if  M  makes  300  and  A  60  revolutions,  both  in  the  same 
direction,  and  the  value  of  i  is  1,  then,  by  using  n  =  a  —  m,  or 
its  equivalent,  n  =  A  +  kt  —  M — 

M  =  60  +  60  X  1  -  300  X  1  =  120  -  300  =  - 180  revolutions 

.'.  )i  =  180  revolutions  in  the  direction  opposite  to  A 

Should  A  and  M  move  in  opposite  directions  at  the  rates  of  60 
and  300  revolutions  respectively,  then — 

)i  =  a  +  m 
or,  n  =  A  +  At-\-  M? 
.-.  7t  =  60  +  60  X  1  +  300  X  1  =  420  in  the  same  direction  as  A 

Thus,  the  fractional  movement  of  n,  due  to  a,  is,  in  the  latter 
instance,  120,  and  that  due  to  m  is  300,  so  that  the  plus  60  has 
become  plus  120,  and  the  minus  300  has  changed  to  plus  that  sum. 


Examples  in   Calculating  the   Length  Wound   upon   the 
Bobbin  with  the  Principal  Types  of  Differentials. 

The  particulars  contained  in  Fig.  23  are  those  existing  in  a 
roving  frame  in  working  condition.  The  particulars  not  given 
in  the  figure  are — The  diameter  of  top  cone,  in  the  part  on 
which  the  centre  of  the  cone  strap  rests,  is  b\\  inches,  and  the 
diameter  of  the  bottom  cone,  also  opposite  the  centre  of  the 
strap,  3/g  inches;  the  diameters  of  the  empty  bobbin  1^^"^,;  inch, 
and  that  of  the  front  roller  1]-  inch.    Under  these  conditions  the 

revolutions  of  the  spindle  per  mhiute  = r- =  11425 

^  ^  33  X  21  ^ 


128  COTTON   SPINNING  CALCULATIONS 

and  the  revolutions  of  the  bobbin  per  minute,  when  the  bottom 
C3ne  is  stopped,  or  when  the  twist  wheel  is  0 — 

40  X  21 

Since  the  two  wheels  in  the  sun  wheel  are  carriers,  and  the  wheel 
on  the  frame  shaft  driving  them  is  36  and  that  driven  by  this 
train  is  also  a  36,  t  therefore  equals  H};  =  1.     Hence  the  revolu- 

40  X  60 
tions  of  the  bobbin  per  minute  =  400  X  1  X  =  1142f 

or  the  same  speed  and  in  the  same  direction  as  the  spindle. 

The  revolutions  of  the  bobbin  per  minute,  when  the  bottom 
cone  is  working  and  the  twist  wheel  is  50,  are 

.,    ,    A. -4-  Tir.N^O  X  60 

or — 

r-/ 400  X  50  X  91  X  23  X  19      400x50x91x  23  X  19  V  .^    1 
LV  1    X35x55xr20xl30"^   1    X35  x55  X  120x  130 /"        J 

40  X  60 
^  40  X  21 

Here  ^  =  1,  and  the  sun  wheel  moves  in  the  opposite  direction 
to  M,  and,  therefore,  the  sign  is  +,  hence 

/o  w  400  X  50  X  91  X   23   X   19     ,    ,^^\      40  x_60 

V  1     X  35  X  55  X  120  X  120  /      40  X  21 

=  revolutions  of  bobbin  per  minute 

=  (57  X  ^  +  400)  X  ^^  =  1306-8 

Therefore,  the  revolutions  of  the  bobbins  in  excess  of  the 
spindles 

=  13068  -  1142-8  =  164 

The  length  of  rove  wound  upon  the  bobbin  per  minute, 
neglecting  the  facts  that  the  rove  is  wound  spirally,  and  also 
that  the  actual  winding  radius  is  greater  than  the  radius  of 
the  bare  bobbin,  is 

=  164  X    r- =  612  inches  per  minute 

lb  X   7 


AND   COSTS   OF   YARN 


129 


the  revolutions  per  minute  of  the  front  roller  being  — ^^ — ^t^ —  > 
^  *=      35x130 

and  the  length  delivered  by  it  in  that  time — 

400  X  50  X  35  X  5"  X  22  ^^^  .  , 
=  1  X  35  X  130  X  4  X  7  =  ^^^  ^^'^"' 
Upon  this  basis  the  bobbin  is  shown  to  wind  7  inches  more 
than  the  actual  length  delivered  by  the  front  roller.  When  the 
amount  due  to  contraction  in  the  roving,  by  reason  of  the  twist 
inserted  in  it,  is  added  to  the  difference  due  to  the  spiral  dis- 
posal of  the  coils,  and  also  to  the  difference  between  the  actual 
radius  of  these  coils  and  that  of  the  bobbin,  the  tension  of 
winding  must  be  considerably  more  than  is  represented  in  the 
calculation. 

The  particulars  contained  in  Fig.  24  are  of  a  roving  frame. 


30      9,0  14  308  revs. 

25     >,ni^^1R  pei^^min. 


Fig.  24. 

the  differential  in  this  instance  being  of  the  Curtis  and  Ehodes 
type. 

Proceeding  to  deal  as  with  Fig.  23 — 

n  =  m  ±  a 
When  M  is  at  rest  it  will  be  seen,  upon  examination  of  this 
differential,  that,  if  the  bottom  cone  is  rotated, 

n  =  a,  or  Kt 
and  in  the  same  direction. 


130  COTTON  SPINNING  CALCULATIONS 

When  A  is  at  rest  and  M  is  rotated, 

n  =  111,  or  M  —  M^ 

and  when  M  and  A  revolve  in  the  same  direction, 

11  =  m  +  a,  or  M  -  Mi  +  At 

Therefore  when  M  and  A  revolve  in  opposite  directions, 

n  =  m  -  a,  or  M  -  lit  —  kt 

The  value  of  t  in  each  of  the  above  instances  is  the  same, 
being — 

30  X  18  X  14 
25  X  30  X  90 

According  to  the  particulars  contained  in  the  figure,  it  mil 
be  seen  that  when  A  is  at  rest, 

n  =  308  -  S08t 

308  X  30  X  18  X  14 


n  =  308  - 


25  X  30  X  90 


The  portion  of  n  denoted  by  a,  when  the  diameters  of  the 
cones  at  the  points  opposite  the  centre  of  the  strap  are — top,  5|, 
bottom  3^  inches ;  equals 

308  X  39  X  5f  X  36  X  46  X   46   x  30  X  18  X  14 
35  X  3i  X  36  X  50  X  106  X  25  X  30  X  90 

M  and  A  are  indicated  in  the  figure  as  working  in  the  same 
direction,  the  flyer  and  the  bobbin  are  also  revolving  in  the  same 
direction,  the  latter  leading ;  the  connecting  sign  between  m  and 
a  must  therefore  be  plus — 


.-.  It  =  (3O8  - 


308  X  30  X  18  X  14^ 


25  X  30  X  90/ 

/  308  X  39  X  5|  X  36  X  46  X  46  x  35  x  18  x  14\ 
\  35  X  31  X  36  x  50  X  106  X  25  X  30  X  90/ 

Under  these  conditions  the  revolutions  of  the  bobbin  per 
minute  will  equal — 

45  X  60 
"  ^  40  X  21 


AND   COSTS   OF   YARX  131 

or — 

F/^QAQ      308  X  30  X  18  X  U\ 
Li^aOS 25  X  30  x~90/ 


4- 


25  X  30  X  90^ 
/308  X  39  X  5|  X  36  X  46  X  40  x  35  x  18  X  14 
\     35  X  3i  X  36  X  50  X  106  X  25  x"W  X  90 


)] 


45  X  60 
^40X21  =  ^^^^^ 


Of  this  sum  the  exact  amount  due  to  the  cones,  signified  by 
a,  is — 

/308  X  39  X  5|  X  36  X  46  X  46   X  35  X  18  X  14\      45  X  60 
V  35  X  34  X  36  X  50  x  106  x  25  x  30  x  90/  ^  40  x  21 

=  87'27  revolutions  per  minute 

The  amount  contributed  directly  from  the  shaft  through  the 
differential,  and  signified  by  m,  is — 


/  308      308  X  30  X  18  X  14\  . .  45  X  60 


=  8791 


\  1  25  X  30  X  90/      40  X  21 

The  revolutions  which  the  spindles  would  make  per  minute 
are 

=  308  X  ^^  =  880 

in  the  same  direction  as  the  bobbin.  Thus,  the  bobbin  leads  the 
flyer  to  the  extent  of 

966-37  -  880  =  86-37  revs. 

This  represents  the  amount  of  rove  wound,  which  should  of 
course  be  approximately  equal  to  that  delivered  by  the  rollers. 
The  revolutions  of  the  front  roller  in  the  same  time  are 

Therefore  the  length  delivered  per  minute  is 
=  92-4  x22  =  290-4 

The  amount  which  the  bobbin  would  wind,  assuming  the 
material  wound  was  |  inch  radius  from  the  centre  of  the  bobbin, 
equals 

86-37  X  li  X  V  =  339-71  inches 


132 


COTTON   SPIXXIXG   CALCULATIONS 


Under  these  conditions  the  290*4  inches  of  rove  delivered  by  the 
front  roller  per  minute  would  be  stretched  to  339'71,  or  to  the 
extent  of 

839-71  -  2904  =  49  31 
this  being  17  per  cent. 

A  noticeable  feature  in  respect  of  the  gearing  in  this  figure 
is  that  the  bobbin  is  not  driven  at  the  same  rate  as  the  spindle 
"uhen  the  cone  drum  ceases  to  bo  a  contributor.  This  makes 
the  correct  adjustment  of  -winding  impossible.  Thus,  when  the 
cone  is  stopped,  the  revolution  of  the  bobbin  per  one  of  the 
spindle  is — 


21  X  33"      /21  X  33  X  30  X  18  X  14 
60  X  33  X  25  X  30  X  90 


r21  X  3^  _  / 
Uo  X  "33      \ 


)] 


45  X  60 
40  X  21 


=  r^i  -    "^^  1      45  X  60      26250  -  2940  .    45  X  60 
Uo      1250 J  ^ 


-60      1250J  '^  40  X  21 
23310  X  45  X  60       999 


75000         ^  40  X  21 


=  0-999 


75000  X  40  X  21      1000 

The  bobbin  moving  slower  to  the  extent  of  O'OOl  per  revolution  of 
the  spindle,  and  thus,  whilst  the  cone  is  stopped,  if  the  spindle 
makes  880  revolutions,  the  bobbin  would  make 

880  X  0-999  =  879-12  revolutions 


T.W.46 


256  revs, 
per,  min. 

'"  ^'^,414850        40 


Ftg.  25. 


The    particulars    given    in    Fig.     25    are    taken    from    an 


AND  COSTS   OF   YARN  133 

intermediate  frame.  The  differential  in  this  case  is  of  the 
Tweedale  type.  Dealing  with  this  as  with  the  previous  ex- 
amples— 

n  =  m  ±  a 

When  M  is  at  rest  and  the  bottom  cone  is  actuated, 

n  =  a,  or  At 

and  in  the  same  direction.    When  A  is  at  rest, 

71  =  OT,  or  M  —  M^ 

When  M  and  A  revolve  in  the  same  direction, 

n  =  m  +  a,  or  M  -Mt  +  At 

When  M  and  A  revolve  in  opposite  directions, 

n  =  ??t  —  a,  or  M.  -  Mt  -  At 

The  value  of  t  in  this  case  is — 

18  X  16 
80  X  48 

Taking  the  speed  of  the  frame  shaft  at  256|  revolutions  per 
minute  with  the  bottom  cone  at  rest — 

n  -  2562  _  256|_x  18  x^e 
''  -  "^""^^  30  X  48 

This  being  the  portion  contributed  to  n,  from  source  m,  when  M 
and  A  are  both  in  action  together. 

That  portion  of  n  contributed  from  source  a,  when  the  dia- 
meters of  the  top  and  bottom  cones — at  the  points  opposite  the 
centre  of  the  strap  during  the  winding  of  the  first  layer — are 
5^  inches  and  3|  inches  respectively,  will  be — 

2562      46  X  57  X  18  X  44  X  18  X  16 
'^  ^  48  X  3|  X  68  X  84  X  30  X  48 
therefore  when  the  M  and  A  are  working  together — 

/  256|  X 18  X  16\      /       ,     46  x  Sj  X 18  X  44  x  18  x  16\ 

n-[Zob,,  30^^/  +  V^^-'  ^  48x3^x68x34x30x48^ 

the  revolutions  of  the  bobbins  being — 

50^^ 
''  ^  42  X  30 


134  COTTON  SPINNING  CALCULATIONS 

The  revolutions  of  the  bobbin  per  minute  are  therefore— 
r(o^a2     256§  X 18  X  16\     f         ^  46  X  5|  X  18  X  44  X  18  X  16^-| 

50  X  55      P/o/rfl.A       ^1  o\  1   OT  ol       50  X  55 

=  (205-3  +  27-3)  X  f^^^  =  508 

The  revolutions  per  minute  which  the  bobbins  would  make 
if  the  bottom  cone  was  stopped  would  be — 

(256-6  -  51-3)  X  ^2-^0  =  ^^^'^^^ 
The  revolutions  of  the  spindles  per  minute  would  be — 

The  revolution  of  the  bobbin  per  1  revolution  of  the  spindle, 
according  to  the  above  working,  is  therefore — 

448148  ^  ^ 
448-148  ~ 

Working  directly  from  the  spindle  to  the  bobbin,  this  last 
result  is  proved  as  follows  : — 

[-30  X  42  _  /30  X  42  X  18  X  16\-i      50  x  55 
L55  X  40      V55  X  40  X  30  X  48/J  ^  42  X  30 
=  revolutions  of  bobbin  per  1  of  spindle 
_  r315^   63  1       50  X  55  _  252  x  50  X  55 
~  L55O  -  550J  ^  42  X  30  ~  550  X  42  X  36 
=  }  =  1  revolution  of  bobbin  per  1  of  spindle 

The  revolutions  per  minute  of  the  front  roller  are — 

2562  ^  46  X   48 
^'^  ^  48  X  130 

The  length  of  rove  delivered  by  the  front  roller  per  minute — 

orA2  ^  46  X   48   X  1"  X  22      __^  .     . 

2564  X  -J7Z zr^rx z =-  =  285  inches 

^      48  X  130  X   1  X   7 


AND   COSTS   OF   YARN 


135 


The  number  of  coils  of  rove  wound  per  minute,  being  the 
difference  in  the  revolutions  as  compared  with  the  spindle — 

=  508  -  448-i48  =  59-85  nearly 
The  length  actually  wound  on  the  bobbin,  assuming  the  radius 

of  the  coils  ~,  1-^   inches  being  the   diameter  of  the  bare 

bobbin,  would  be — 

=  59-85  X  i-— ^^^  =  305-6  inches 

8x7 

Thus  the  length  of  the  rove  wound  on  the  bobbin  exceeds  that 
delivered  by  the  roller  to  the  extent  of  305-6-285,  or  20-6 
inches,  equal  to  7*2  per  cent. 


Fig.  2G. 

In  Fig.  26  the  differential  is  that  known  as  the  Fallows 
motion.  The  particulars  herewith  given  are  of  a  slubbing 
frame.  This  differential  differs  considerably  from  the  usual 
types,  and  an  explanation  of  its  action  is  deemed  advisable. 

The  right  extreme  of  the  portion  marked  A  consists  of  a  cam, 
the  face  of  this  bears  against  the  side  of  a  disc  formed  upon  the 
rim  of  a  double  wheel.  Wi  and  W2  denote  the  left  and  right- 
hand  sides  of  this  disc  wheel.  The  teeth  are  of  special  design, 
and  the  wheel  is  mounted,  loose,  on  a  spherical  bearing.  This 
spherical  bearing  is  secured  to  the  driving  shaft.  This  form  of 
bearing  admits  of  a  portion  of  Wi  being  in  gear  at  a  point  with 
M,  and  a  portion  of  W2  also  in  gear  at  a  point  with  N,  but  on 
the  opposite  side  of  the  axis.     Thus,  the  double  wheel  gears  and 


136  COTTON   SPINNING  CALCULATIONS 

worbs  in  an  oblique  position,  and  this  is  maintained  by  the 
pressure  of  the  cam  against  the  sides  of  the  disc.  Under  these 
conditions  Wi  and  W2  act  as  a  compound  wheel  toward  motion 
passing  from  M  to  N.  Under  these  conditions  the  value  of  the 
train  would  be — 

=  K      ^ 
Wi  ^   N 

The  effect  of  the  movement  of  A,  when  M  is  at  rest,  is  that 
the  cam  would  compel  the  gearing  points  of  Wi  and  W2  to  circu- 
late, the  teeth  of  the  former  entering  and  emerging  from  the 
teeth  contained  in  M  as  A  revolves ;  therefore  if  Wi  contains 
the  same  number  of  teeth  as  M,  no  circumferential  motion 
of  Wi  or  W2  could  accrue.  This  reasoning  applies  in  a  similar 
manner  to  W2  and  N.  Should  M  and  Wi  contain  different 
numbers  of  teeth,  then  circumferential  motion  will  be  imparted 
to  Wi  and  W2  in  the  direction  opposite  to  that  of  A,  when  Wi 
contains  less,  and  in  the  same  direction  when  Wi  has  more, 
teeth  than  Wg.  Thus,  the  movement  of  Wi  would  be  Wi  —  M, 
in  teeth  per  revolution  of  A,  and  its  rotary  movement  would  be — 

Wi  -  II 
Wi 
The  movement  in  teeth  made  by  W2,  in  the  same  time,  would 
be— 

Wi  -  M      W2 

Wi      ^    1 
and,  therefore,  if  N  contained  the  same  number  of  teeth  as  W2, 
the  movement  of  N  would  be  the  same  as  W2. 

If  the  number  of  teeth  in  W2  and  N  were  not  alike,  the 
movement  would  be  further  affected  by  reason  of  the  cam  A 
causing  all  the  teeth  in  W2  to  enter,  and  emerge  from,  as  many 
of  those  in  N  as  are  contained  in  W2.     Thus,  the  action  in  this 
case  must  be,  when  M  is  at  rest  and  A  makes  one  revolution — 
=  ^Vi-M      W2      N  -  W2 
Wi"     ^   N  "^       N 
In  this  differential  t  has  two  values.     In  respect  of  the  motion 
from  M  its  value  is — 

M       W2 

W  ^  N 


AND   COSTS   OF   YARN  137 

Let  this  be  termed  ti.     "When  the  motion  is  from  A  its  value  is — 
Wi  -  M      W2  ,  N  -  W2 
Wi  N  ^       N 

Let  this  latter  be  denoted  by  fa- 
it will  now  be  possible  to  proceed  to  deal  with  this  in  the 
same  manner  as  with  previous  examples — 

n  =  111  ±  a 
under  all  conditions. 

Therefore  when  A  is  at  rest — 

n  =  M^i 
in  the  same  direction. 

When  M  is  at  rest — 

n  =  Af2 

the   resultant   direction  depending   on   the   differences   in   the 
number  of  teeth  contained  in  the  wheels  M,  Wi,  W2,  and  N. 
This  will  be  indicated  by  the  sign  being  either  plus  or  minus. 
When  M  and  A  revolve  in  the  same  direction  together— 
n  =  Mti  +  A?2 
Taking  the  particulars  of  the  gear  as  contained  in  Fig.  26,  and 
the  diameters  of  the  cones  at  the  j)oints  opposite  the  middle  of 
the  cone  strap,  when  the  first  layer  is  being  wound,  as  follows  : — 
top  11  inches,  bottom  3;|  inches,  and  that  of  the  bare  bobbin 
li  inch;  then:  the  revolutions  of  the  bobbin  per  minute  when 
the  twist  wheel  is  0,  or  when  the  bottom  cone  is  not  engaged, 
would  be,  according  to  the  formula — 

165  X  3-2  X  36  X  63  X  50         ^r^n  onn 

1     X  3b  X  36  X  58  X  2b 

The  revolution  of  the   bobbin  per  minute  with  a  50  twist 
wheel,  assuming  M  to  be  at  rest  whilst  A  is  in  motion — 

_  rl65x46x7^x26x80.36-32     36      36-36 H      63^50 
~  L  1    x24x3|jx75x50V     36^^36"^      36     Jj  ^  58  x'26 
_  165  X  46  X  57  X  26  X  8  X   4   x  63  x  50  _ 
~    1    X  24  X  27  X  75  X  5  X  36  X  58  X  26  ~ 

Therefore  the  revolutions  per  minute  of  the  bobbin  during 
the  winding  of  the  first  layer  would  be — 

=  306-366  +  85-95  =  392-316 


138  COTTOX   SPINNIXG  CALCULATIONS 


or — 


1-165  X  32  X  36     /165  x  46  x  7^  X  26  x  SOV  36  -  32     36     36-36\-i 
L  1    x36x36'^V  1    x24x3tx75x50A     36     ^36^     36     /J 

x|^^-^?  =  392-316 
58  X  2o 

The  revolutions  of  the  spindle  per  minute  are — 

^f  '"'.I'^f.  =  306-306 
1     X  58  X  2o 

The  number  of  coils  of  rove  \Y0und  upon  the  bobbin  per 
minute  are  therefore — 

=  392-316  -  306-366  =  85*95 
The  following  will  therefore  represent  the  length  of  rove  wound  : — 

1-  X  22 

85-95  X  -^-= —  =  405-193  inches  per  minute 

The  front  roller,  in  that  time,  makes — 

165  X  46  X  40  ,   ,. 

fr. T-,  r-  revolutions 

24  X  115 

or  delivers — 

165  X  46  X  40  X  It  X  22      ^^_  noo  •     i, 

^, ^^^ ^ =  388-928  mches  of  rove 

24  X  Ho  X  7 

Therefore  that  length  is  stretched,  if  the  rove  is  assumed  to 
have  no  thickness,  to  405-193  inches,  or  to  the  extent  of 
13-265  inches  more  than  the  rollers  deliver;  this  is  equal  to 
nearly  4|  per  cent. 

The  particulars  contained  in  Fig.  27  are  those  of  a  slubber 
frame,  the  differential  being  that  known  as  Brooks  and  Shaw's. 
The  action  of  this  differential  is  readily  understood.  Applying 
the  formula  as  in  the  previous  examples — 

n  =  m  ±  a 
for  all  conditions  of  working,  the  revolutions  which  the  bobbin 
would  make  per  minute,  if  the  bottom  cone  was  stopped,  or  if 
the  twist  wheel  was  0,  are — 


,     ^    ,      74  X  50 
=  ^"  ±  '^  ^  5^^4 


AND   COSTS   OF   YAEN 


139 


Here — 


[0±( 

-( 


m  =  Mt 
a  =  k  —  At 
_  30  X  18 
^  ~  18  X  37 
M  =  200,  and 
A  =  0 
200  X  46  X  6|il  X  30  X  20  X  56n 
X  32  X  3^    X  41  X  40  X  64. 


200  X  46  X  6f  ji  X  30  X  20  X  56  X  30  X  18 
X  41  X  40x64x18x37 


32x3i 


)] 


74x50      ,^^^ 
X  =7, — ^,  =  100-5 
52  X  24 


The  sign  ±  in  the  last  instance  is  determined  by  the  directions 
of  M  and  A ;  when  they  move  in  the  same  direction  it  is  + , 
and  when  opposite  it  is  —  . 


Fig.  27. 

The  revolutions  of  the  bobbin  per  minute,  when  the  cone 
strap  is  in  the  initial  position  and  M  and  A  are  in  motion,  as  per 
conditions  in  the  figure,  may  be  ascertained  by  adding  the  speed 
under  the  two  sets  of  conditions  together,  i.e. — 

480-77  4-  100-5  =  581-27 


obtained  as  follows  : — 


r200  X  30  X  18  ^  /200j<  46  x  61-1  x  30  x  20  x^6^ 


18  X  37 


32  X   3i  X  41  X  40  X  64. 


_  1^200  X  46  X  6|i^  X  30  X  20  X  56  x  30  x  18\-i  .  74  x  50 


32  X  U   X  41  X  40  X  64  X  18  X  37/ 


52  X  24 


140  COTTOX   SPIXXIXG  CALCULATIONS 

therefore,  of  these  the  bobbin  -^ould  make — 

/200  X  30  X  18\.  ^\      74x50       ,^^,f,         ,    , .  '  .     , 

(  -^i T7^ — 7^  ±  0  )  X  -^c — 277  =  480]  y  revolutions  per  minute 

V  1    X  18  X  37        ^      £)2  X  24  ^ "  ^ 

Calculating  directly  from  the  spindle  to  the  bobbin,  the  revolu- 
tions of  the  latter  per  one  of  the  former  would  be — 

/24  X  52  X  30  X  18  ^  ^\      74  X  50      , 
±  0     X  -^ ^  =  1 


\50  X  60  X  18  X  37  ~     /       52  x  24 

The  revolutions  of  the  bobbin,  assuming  the  bottom  cone  to 
rotate  whilst  M  is  at  rest  and  the  diameters  of  the  top  and 
bottom  cones,  at  points  opposite  the  centre  of  the  cone  strap 
whilst  in  the  initial  positioji,  being  G\\\  inches  and  3i  inches 
respectively,  would  be — 

=  [162-162  +  (179-177  -  145-278)]  x  14^^ 

=  (162-162  +  33-899)  x  L^      T:  =  581-27 

The  rate  at  which  the  coils  are  wound  during  the  first  layer 
laid  upon  the  bobbin  is  therefore — 

581-27  -  480-77  =  100-5  per  minute 
The  rate  at  which  the  rove  is  wound — 

100-5  X  1^  X  '---  =  473-78  inches  per  minute 
The  rate  at  which  the  front  roller  revolves — 

46  X   65 

200  X  q5 :r^  revolutions  per  minute  =  1431 

oA  X  -LoU 

The  length  delivered  per  minute  by  the  front  roller  is — 

„„„       46  X   65       lyV  X  22       ,„^^.     , 
200  X  ^ -^  X  -^^ =  480-0  inches 

oZ  X  ioU  / 

The  amount  of  rove  which  the  bobbin  winds  in  excess  of 
that  delivered  by  the  front  roller,  assuming  the  radius  of  the 
winding  circle  of  the  rove  f  inch — 

=  480  -  473-78  =  6*22  inches 
or  1-3  per  cent,  less  than  that  delivered. 

The  Speed  in  Fly  Frames. — The  speed  at  which  the  most 
satisfactory    results     are     obtained    var}-    with    the     working 


AND   COSTS   OF    YAllN  141 

conditions :  the  kind  of  work,  the  efficiency  of  the  machines, 
skill  and  organization  of  the  operatives. 

Data  on  this  suhject  should  not  be  regarded  as  inflexible, 
but  should  be  subjected  to  modification  such  as  experience  and 
developments,  in  the  application,  suggest. 

The  rates  of  spindle  speeds  attainable  in  modern  makes 
of  these  frames,  fitted  with  long  collars,  are — 


Kind  of  cotton. 

Slubber. 

Intermediate. 

Rover. 

Jack. 

Egyi)tiau 

450-50U 

G50-800 

950-1050 

1 000-11. jQ 

American 

550-700 

700-850 

1050-1200 

Indian 

tJOO-700 

750-850 

10.50-1200 

Adopt  the  highest  beneficial  speed  and  fix  other  conditions  so 
that  the  whole  of  the  machinery  is  continuously  occupied  in 
producing  the  required  amount. 

Proportions  of  Machinery  in  the  Carding  Department. — The  fly- 
frame  processes  usually  consist  of  three  stages,  but  sometimes 
two  and  four  are  adopted.  They  are  named  respectively  :  slubber, 
intermediate,  rover ;  slubber,  rover ;  slubber,  intermediate, 
rover,  jack. 

The  number  of  these  processes  expedient  depends  upon  the 
extent  of  the  attenuation  desired  prior  to  spinning,  and  also,  to 
some  extent,  upon  the  character  of  the  cotton.  Uniform  stapled 
cottons  are  influenced  less  detrimentally^  by  high  drafts.  Bej^ond 
a  certain  count  the  roving  can  be  more  economically  prepared  by 
an  additional  process.  That  limit  cannot  be  fixed.  It  ranges 
upwards  from  between  15  and  20.  The  draft  necessary  to 
attenuate  the  drawing  sliver  to  the  desired  extent  for  sj^inning 
is  distributed  amongst  these  two,  three,  or  four  processes  in 
certain  proportion  (see  p.  142). 

In  the  machinery  from  the  card  onward  to  spinning  it  is 
customary  to  arrange  the  machinery  in  what  are  termed  "  pre- 
parations."  A  "preparation"  consists  of  one  slubber  and  all 
the  other  machinery  necessary  to  prepare  as  well  as  to  deal 
with  its  product.     Such  may  be  literally  expressed  as  a  slubber 


142 


COTTON   SPINNIXG   CALCULATIONS 


and  its  complement.     The  following  are  the  proportions  of  the 
machinery  forming  one  preparation  in — 


Cards. 

Combers. 

1 
Draw  frames.          Slubbers.       |  Intermediates.           Rovers. 

Mule    spin- 

9 to  1.3 

6  to  10 

One  frame  of   One  frame  of   Two  frames 

Four  frames 

ning 

18    to     24 

80    to    100     of    120    to 

of  1G8  to  200 

dels,    divi- 

spindles          140  spdlea. 

spindles  , 

ded       into 

each 

each. 

three  heads 

Bing  frames 

Ditto     Ditto 

Ditto 

Ditto                Ditto 

Five   frames 

of  168  to  200 

1 

spindles. 

The  following  are  therefore  the  proportions  of  the  above- 
named  machines  per  slubbing  spindle,  respectively : — 

(deliveries)       (spindle)      (spindles)  (spindles) 

0-1125-0-15     0-075-0-1     0-075-0-01     VO    2-72-3-0     S-O-IO'O 

These  proportions  are  those  ruling  in  the  bulk  of  spinning 
mills,  and  it  is  therefore  reasonable  to  assume  that  they  repre- 
sent what  is  found  most  useful. 

Drafts  in  Fly  Frames. — The  following  are  the  factors  control- 
ling the  division  of  the  combined  attenuation  required  in  the 
respective  fly  frame  processes  : — 

(1)  Number  of  spindles  of  each  type  available  ; 

(2)  Speeds  practicable ; 

(3)  Extent  of  the  combined  attenuation  required ; 

(4)  Efficacious  twist  constant  at  each  stage ; 

(5)  Time  lost  at  each  stage. 

These  decided,  for  example,  as  given  below,  the  respective 
drafts  are  arrived  at  as  follows  : — 


Speed  of  spindles  (per  minute). 

Slubber,  550. 

Intermediate,  800. 

Rover,  1200. 

Per  cent,  time  lost  (approx.) 
Twist  constant     .... 
Proportions  of  spindles 
Count  at  each  stage      .     . 
Draft  at  each  stage  .     .     . 

1.5 

1 
1 

c, 

10 
1 
3 

c. 

7 
1 
8 
Ca 

^3 

Total  draft   in   these   fly  1 
frames                                  j 

This  is  always  fixed  by  the  count  of  roving 
decided  upon  for  spinning  and  by  the  weight  of 
sliver,  most  suitable,  at  the  drawing  frame. 

AND   COSTS    OF   YAKN  143 

]rHJi  fixed  quantities  of  fiy  frames  and  S2)in)iin(j  niacltincrij 
available,  tJie  adoption  of  the  most  suitable  spindle  speeds  decide 
the  drafts  by  fixing  their  capacity  in  respect  of  their  twisting 
rates.  The  demands  of  the  spinning  machines  having  been 
ascertained,  the  highest  rate  at  which  the  roving  spindles 
can  be  satisfactorily  run  will  decide  the  most  suitable  count 
of  roving  to  prepare  and  also  the  draft  in  the  spinning  machine. 
Let  the  count  of  roving  be  denoted  as  x  lbs.  per  spindle,  and 
C3,  C2,  Ci,  the  counts  of  the  roving,  intermediate,  and  slubbing, 
respectively ;  then  the  amounts  required  from  the  intermediates 
and  slubber  will  be — 

8c 
Intermediate,  3  per  8  roving,  spindles,  -^ 

o 

8a; 
Slubber,  1  per  8  roving,  spindles,  — 

Hence  the  following  equations  : — 

Roving — 

1200  X  -^^ 

-— = ^^^ =  X  lbs.  per  minute  per  spindle 

VCg  X  C3  X  36  X  840  ^  ^        ^ 

Intermediate — 

800  X  tKir 8.^3  „  .      .  .    ,, 

Slubber— 

550  X  — -- 

— — — LOO _  g,^  Y\)B.  per  minute  per  spindle 

x/Ci  X  Ci  X  36  X  840  ^  ^       '- 

From  the  above  equations  the  separate  values  of  Ci,  C2,  and 
C3  may  be  found,  when  the  sum  of  the  draft  involved  in  this 
production  is  known.  The  sum  of  the  drafts  in  the  rover, 
intermediate,  and  slubbing  frames  is  found  by  ascertaining 
the  weight  per  yard,  or  count,  of  the  sliver  at  the  finishing  head 
of  the  draw  frame  that  will  produce  the  required  weight  when 
running  at  the  most  desirable  speed,  and  comparing  this  with 
the  count  of  roving  required. 

An  example  is  provided  by  assuming  the  conditions,  in 
respect  of  the   counts,  deUvered,   at  the  drawing  and  roving 


144  COTTON  SPJNNING  CALCULATIONS 

frames :  0"2  and  &0  respectively.     Under  these  conditions  the 
total   draft   or   the  attenuation   in   the   slubber,   intermediate, 

and  roving  frames  would  be  =  -^  x  (2  X  2),  the  latter   allow 

for  the  two  doublings  in  each  of  the  latter  stages ;  =  120. 

Therefore   the    weight    produced    per    roving    spindle    per 
55  hours 

55                      60    X  1200  X    93        ^  .^  „ 
= y  -~-^ =  8'3  lbs. 

36  ins.  X  840  yds.      x/6         6         100 
(C3)       (C3) 

The  weight  produced  per  intermediate |  _  ^       q-q  11 


=  ^  X  8-3  lbs. 


spindle  per  55  hours  j       3 

55  X  60  X  800  X  90 
36^X  840  X  -V/C2  X  C2  X  100       3 

.^    _  55  X    60    X  800  X  90  X  3   _  - 

•'•     ^'^^'  -  36  X  840  X  100  X  8  X  8-3  ~  "^ 

.•.     Co  =  2-33,  the  count  of  the  intermediate  rove 

The  weight  produced  per  slubbing)  _  0.0  w  8 
spindle  per  55  hours  j  ~  1 

55  X  60  X  550  X  85 

36  X  840  X  -v/CT  X  Ci  X  100 

yyr      n  55  X  60  X  550  X  85       _  „.,.^_ 

•'     V  ^1  X  Oi  -  3(3  X  840  X  8-3  X  8  x  100  "  "  ^^^ 

.-.     Ci  =  0*725,  count  of  the  slubbing  sliver 

The  drafts  in  the  respective  fly  frames  may  be  now  ascer- 
tained from  the  above  counts,  and  they  are  as  follows  : — 
Draft  in  the  rover — 

count  of  roving  X2     _6x2      ^.„ 


=  8-3x8  lbs. 


count  of  intermediate        2'33 

Draft  in  the  intermediate — 

count  of  inter,  rove  x  2  _  2*33  x  2 
count  of  slubbing       ~     0"725 


=  6-43 


AND   COSTS   OF   YARN 


145 


Draft  in  the  slubber — 

count  of  slnbbing  _  0*725 
count  of  sliver  0'2 


=  3-G25 


It  is  seen,  from  this  procedure,  that  the  drafts  in  these 
machines  depend  not  only  upon  the  proportions  of  spindles,  but 
also  on  the  other  productive  factors  mentioned  on  p.  142,  and 
numbered  2,  3,  4,  5. 


Particulars  of  Fly  Fbames, 


Machine. 


Eover  .  .  . 
Intermediate 
Slubber     .     . 


Loss  of  time 

due  to  oiling, 

cleaning,  and    Usual  sizes 
incidental  of  full 

stoppages         bobbins, 
apart  from 
dofiSng. 


Usual 
gauge?. 


Usual  lift= 


Contents  in 

ounces  per 

bobbin. 


SP/o 


4i"  to  4J" 
5f" 


Time  lost 
per  doff. 


]i"  to  3f "  !  5"  to  51"    7"  and  8"    8  to  11  oz.s.    12  mins. 


6"to6J"    9"  and  10";  18to24ozs. 
9"        j  10"  to  12"    24to30ozs. 


The  Production  in  Fly  Frames. — To  estimate  the  production  of 
the  above-named  machines.  Eover,  spindles  making  1150 
revolutions  per  minute ;  hours  worked,  55.  Allow  5^  per  cent, 
for  loss  occasioned  through  breakages,  and  proceed  as  follows  : — 

Weight  of  contents]     -.qq     [the  weight  that  would  be  delivered 
of  full  bobbin  ii^f  ^(n.^~l     ^^  *^®  period  required  to  make  a 
)     "  "^  ^     (     doff,  if  no  stoppages  =  {x) 

the     weight     in     ounces 
_  I     delivered  by  the  roller 
in  one  minute,  uninter- 
rupted vi^orking  =  (.?/) 


ounces 


1150  X  16 


twist  per  inch  x  36  x  840  X  count 


55  X  60 


=  minutes  required  to  fill  a  set  of  bobbins 

y 

■X   .    ,.       1     .  •     1  ft-  r  minutes  taken  to  fill  and 

-  +  time  lost  m  doflmg  =  {     ^^g-  ^  ^^^  ^^ ^^^^-^^  ^  ^^^ 

/weight  of  contents  oh  _  ^production  per  spindle  in 
^  a  bobbin  in  ounces  /  ~  t     ounces  per  week 


146  COTTON   SPINNING   CALCULATIONS 

Therefore,  with  the  count  produced  by  the  roving  6,  the  twist 
constant  1*2,  and  the  contents  of  a  full   bobbin  10  ozs.,  the 
production    per    spindle   in  ounces  and  hanks  per   55   hours, 
respectively,  would  be — 
55  X  60 


100 

10    X   ^rT:v 


1150  X  16 


\/6  X  1-2  X  36  X  840  X  6 


X  10  =  103-52  ozs. 


Hanks  =  l°«-:f^-«  =  38-8125 
lb 

With  the  count  produced  by  the  intermediate  2-33,  the  twist 
constant  1*2,  and  the  contents  of  a  full  bobbin  22  ozs.,  the 
production  per  spindle  in  ounces  and  hanks  per  55  hours 
respectively,  would  be — 

55  X  60 ^ 

100  / 

""  94-5 +  12      X  22  =  ^11^^22  =  294  ozs. 

800  X  16 Zd5  +  iZ 

^2-33  X  1-2  X  36  X  840  x  2-33 

^     ,         294  X  2-33       .o  Q 

Hanks  = ^- —     =  42-8 

lb 

With  the  count  produced  by  the  slubber  0"715,  the  twist 
constant  1*2,  and  the  contents  of  a  full  bobbin  28  ozs.,  the 
production  per  week  in  ounces  and  hanks  per  55  hours 
respectively,  would  be — 

55  X  60  ^ 


28  X^ 

^^  ^  94-5        +  12  r^  ^^  "  ^^^^  ^^^• 


550  X  16 


V^O-725  X  1-2  X  36  X  840  X  0-725  J 

„     ,  1055  X  0-725        ,„ 

Hanks  = z.^ =  47 

lb 


AND   COSTS   OF   YARN 


147 


Examples  of  arranging  the  speeds,  drafts,  and  counts  to  suit 
the  mill  specification.  The  following  being  the  quantities  of 
each  kind  of  machinery,  ascertain  the  suitable  speeds,  drafts, 
and  counts. 

Spinning  spindles,  mule — . 


32  pairs  weft  IJ"  gauge,  64"  +  4"  draw 
IG 


twist  If 


Total  spindles 


Spindlea. 

83,688 
34,488 

118,176 


The  weft  are  engaged  upon,  average  counts,  46^ 
„     twist  ,,  ,,  „  36' 

The   production  of  these   per   55. j   hours  would   be   about 
27i  hanks  of  46^  W. ;  29i  hanks  of  36'  T. 

The  other  machines — 


Roving. 

Intermediate. 

Slubber. 

Dr.  F.R. 

Cards. 

Scutchers. 

Number  of  frames 

Spindlea  or  beads 

Gauge    .... 
Lift 

60 

176 

8  in  20f' 
7" 

24 

140 

8  in  26" 
10" 

12 

96 

4  in  19" 
10" 

12 

(3  beads  2  x  4| 

\of  8  dels,  each/ 

18 

120 
45" 

8 

4  laps  up 

45" 

Reasonable  allowances  in  such  a  mill — ■ 


Doffing, 
mins. 

Cleaning. 

Stoppages. 

Other  loss. 

Weight  on  bobbin. 

hrs. 

mins.  per  doff 

per  cent. 

07.S. 

Mule     .... 

8 

'^ 

— 

^ 

— 

liovers  .... 
Intermediates     . 

12 

12 

•> 

U 
22 

Slubbers    .     .     . 

14 

ft 

14 

" 

28 

Suitable  roving  for  the  above  counts  of  yarn  :  5^  for  weft  and 
4i  hank  for  the  twist. 

The  relative  productive  rates  in  the  roving  frames — 

Count  5^  X  y/5^  =  time  per  lb.  5^ 
„      4^  X  ^U  =  „  U 


148  COTTON   SPINNING  CALCULATIONS 

If  all  5^-liank  rovings  were  produced,  the  total  weight 
would  be — 

28160_Xv/:4L  >^  =20,777  lbs.  +  50,280  lbs.  =  71,057  lbs. 

The  amount  of  4^-hank  roving  required  per  week  is 
28,160  lbs. 

The  number  of  roving  spindles  required  to  prepare  50,280  lbs. 

of  5i-hank  must  be — 

50280 
10,560  total  roving  spindles  x  rfjonrj  =  7472,  say  42  frames 

Leaving  18  frames  for  the  4^  hank. 

Another  way  of  arriving  at  the  number  of  roving  spindles  to 
engage  on  each  count  is — 

50,280  lbs.  of  5i  hank  =  276,540  hanks 
28,160  lbs.  of  41     „      =126,720      „ 

403,260      „ 

Therefore,  if  60  frames  of  176  spindles  produce  the  above, 
and  the  respective  productive  ratios  are — 

For  4^^  4:}j  X  v^5i  in  hanks  or  length 

then  the  number  of  frames  required  for  126,720  hanks  of  4J* — 

-  60  x^^^^™x^^- 18  frames 
-^^"^  403260  ^  ^51  " 

and  for  276,540  hanks  of  5^^— 

=  60  X  ?L6|40  ^  VSi  ^  ,2  ,^^^^^ 
403260      ^4^ 

The  production  of  the  fly  frames,  drawing  frames,  and  cards, 
in  pounds,  must  be  as  follows,  allowing  i  per  cent,  for  waste  at 
each  stage : — 

5^  hank  :  Production,  in  pounds,  per  roving  spindle — 
50280    X  100  _ 
42  X  176  X  99h~ 


v^^^^i^ 


AND   COSTS   OF   YARN  149 

U  hank  :  Production,  in  pounds,  per  roving  spindle— 

21860  j<JOO_       ; 
18  X  176  X  991  ~  8-93 

Production,  in  pounds,  per  intermediate  spindle.     All  these 
frames  making  the  same  count— 

78440  X  100 
3360   X   99  ~ 

Production,  in  pounds,  per  slubbing  spindle— 
78440  X  100  _ 
ll52"x  98i~  ^^'^^ 

Production,  in  pounds,  per  draw  frame  delivery— 
78440  X  100 
~96~>r98~  =  S^4  lbs. 

Weight  per  card  (see  later). 

The  Speeds  of  the  Spindles  in  the  Roving  Frames.— Takin^r  the 
twist  constants  at  1-2  in  each  of  the  fly  frames,  and"  the 
stoppages  and  allowances  as  indicated,  proceed  to  ascertain 
the  rate  of  rotation  of  the  spindles. 

Eoving,  51  hank  :  The  doffs  per  week— 

The  time  to  complete  a  set  of  bobbins  and  doff— 

97- 
^  (551  -  21)- ~  -  119-28  (mins.  per  doffing) 

9^94  =  5  hours 

Speed  of  spindles ;  revolutions  per  minute— 

.  11  X  51  X  840  X  36  X  ^51  X  1-2 

"  16  5~>r60  "  =  ^^^^ 

Koving,  41  hank  :  The  doffs  per  week— 

8-93  X  16      _ 
-  J-J--   =  12-993 


150  COTTON   SPINNING  CALCULATIONS 

The  time  to  complete  a  set  of  bobbius  and  doff- 

Q7J- 
(55L  -  2i)^  -  12-993  X  12  mins.        ^^.^ 


^^^ =  T^^.  =  3-78  hours 

12-993  12-993 


The  Count  of  the  Intermediate  Roving. — The  weight  on  an 
intermediate  bobbin  =  22  ozs. 

Eevolutions  of  spindle  per  minute,  800 ;  allowances :  12 
minutes  each  doff,  and  2|-  per  cent,  after  2i  hours  for  cleaning. 

rr,.  1         ,     .  -.      rv>  23-6   Ibs.    X    16  .^  ^^..  . 

Time  lost  m  doffing  = ^ X  12  =  206  mms. 

97I- 
Nett  time  working  =  53  hrs.  -  206  mins.  x    ^r^  =  2887  mins. 

•'•  ^^'  ^^^^^*  =  24-3  X  7000 
2887  X  800 
l-2\/Cx  36  ) 
25  X  2887  X   800 


3   X  24-3  X  7000  X  v/C  X  12  x  36 
2-63 


The  count  = 

:.  count  X  \/count  =  2'63 
.'.  count  =  1-90 

The  Count  of  the  Slubbing  Rove. — The  weight  of  the  slubbing 
bobbin  =  28  ozs. 

Eevolutions  of  spindles,  600 ;  allowances  :  14  minutes  per 
doff,  and  2i  per  cent,  after  2^  hours  for  cleaning. 

The  production  required  per  spindle  per  week  =  69"  12  lbs. 

Time  lost  in  doffing  = ^^^ x  14  =  553  mins. 

971 
Nett  time  working  =  53  hrs.  -  553  mins.  x  —^  =  2547  mins. 


AND   COSTS   OF   YARN  151 

The  count  =  gcj-ic/x  7000 
f  '2547  X  600 
I  l-2v/Cx  36  ) 
25  X  2547   X   600 


The  count 


3   X  69-12  X  7000  X  1-2  X  V'C  X  36 

0-663 


Count  X  v/count  =  0-737 

The  Count  of  the  Sliver  at  the  Drawing  Frame.— Third  head  ; 
weight  per  dehvery,  834  lbs.;  speed  of  F.Pw,  320;  1-^  inch 
diameter ;  allowances  :  2^  hours  for  cleaning  and  2^  hours  for 
breakages. 

Length  delivery  per  week  in  yards 

=  320  X  ^  X  ^   X  60  X  53  X  ^^^ 


Weight  of  the  sliver  delivery  in  grains  per  yard 

_  834j^7_000^^^^6j<^2O00  ^  ^^        .^^^ 
~  320  X  It  X  22  X  60  X  53  X  97i 


Drafts. 
The  Drafts  up  to  this  stage. 

Slubber  =      ^  ^^    ^^  =  4-33 

Intermediate  =     ^  rron     =5-16 
u-  tot 


Piover  for  5h  =  -^^rrr-  -  5 
^  1-9 

Rover  for  4^  =    -^.  .^      =  4-73 


1-9 


152 


COTTON   SPINNING  CALCULATIONS 


Weight  of  Card  the  Sliver. — Number  of  cards,  120 ;  allow  4  for 
grinding.     Hours  worked,  actual,  55,  less  2h  per  cent. — 

78440  ^  100      ^^„  „ 

-j^  X  -^Y  =  ^97  lbs.,  say  700 

Revolutions   of  doffer  15   per   minute  26  inches  diameter. 
Weight  of  sliver  per  yard — 

7000  X  700  . .  „        ■ 
ofi — oo cvfi =  ^^'7  grams 


Analysis  of  the  Action  of  Deawing  Rollers. 

Provided  it  is  reasonable  to  assume  that  top  rollers  move 
at  the  rate  of  the  cotton  with  which  they  are  in  contact,  then 
Figs.  28  and  29  are  records  of  the  action  of  the  drawing  rollers 
in  the  various  frames,  under  ordinary  working  conditions. 

Fig.  29  gives  the  particulars  of  the  observed  relative  move- 
ment in  slubber,  intermediate,  roving,  and  spinning  machines. 


Draft:  -^1045-^<-5-7  -^ 

Revs:  37  33  63 


Cir;         f71  mm]     p4  mmA  p2  mm., 

fv  y  tv  yv  y^ 

Dpaft;0-96>^-<1-15>— <       >— CIO 


Revs:  10  8-5  41f 

Draft:  .^  i -24 -^<-5-2-^ 

Fig.  28a. 


Cir:       >  (80  ni m  V  |70  m m)  (80  m m . 
Revs:  31|-  40^  ^if-^ 

Draft:  _j_i.255-^-^502-^ 

Fig.  28b. 


Those,  subsequently  given,  marked  S.W.  being  of  the  self- 
weighted  type,  i.e.  only  the  front  top  roller  being  weighte.i. 
The  rest  are  of  the  ordinary  weighted  type. 

Figs.  28a,  28b,  show  the  manner  of  obtaining  the  data. 
The  revolutions  given  are  exclusively  in  respect  of  each  pair 
of  rollers  (bottom  and  top).  The  relative  rotation  of  the 
different  lines  are  contained  in  the  draft. 

In  these  figures  the  rollers  are  arranged  in  the  order  of  their 


AND   COSTS   OF   YARN  153 

sequence,  from  left  to  rigbt,  back  to  front.  Their  circumference, 
revolutions,  and  draft  are  placed  opposite  the  parts  to  which 
they  refer. 

The  top  line  of  numerals,  in  figs.,  are  the  observed  ratio  in 
the  movement,  or  draft,  in  the  top  rollers,  in  each  instance  in 
terms  of  one  of  the  precedent  roller.  Thus,  1'003  is  that  of  the 
second  in  terms  of  1  unit  of  movement  of  the  first  top  roller. 

The  middle  line  of  numerals  relate  to  the  difference  in  the 
movement  of  the  top  and  the  bottom  rollers  in  terms  of  one  of 
the  latter. 

The  bottom  line  of  numerals  gives  the  ratio  between  the  bottom 

SLUBBER  INTERMEDIATE  ROVER 

^1-15  -^4-32-^  ^1.045^5-7-^  ^V013^3.98-^ 

1-015  107  0-982    0-962  Vie  1008       1-0  1-205  1-0 

Vl-218-J<~3-97j  V-T  255^:^5  02 -J'  V-1-21  5  J«_3-31-5y 

ROVER  (S.W.)  RING  FRAMECS.W.) 

1'003-^P$—  6-4  -^  fg-  108  ->T<  -7-05->» 


^V003-^6-4-^  ^1-08-^ 

1-(l  1-287  1-005  1-Q2  1-125  10 

lU-l  24  -i-  5  2  -i  >L  1  21  JU^6  36  -J 


Fig.  29. 

lines  of  rollers,  in  each  instance,  in  terms  of  one  of  the  precedent 
roller. 

The  features  most  noticeable,  fig.  29,  are  the  variations  in  the 
slip  of  the  cotton,  indicated  by  the  movement  of  the  respective 
top  rollers.  Except  in  the  slubbing  frame,  this  slip  is  consider- 
able. With  that  exception  the  effect  of  the  action  of  the  first  and 
second  pairs  of  rollers  appears  to  be  only  that  attributable  to  the 
elasticity  of  the  rove,  being :  4"5  per  cent,  in  the  intermediate, 
1'3  per  cent,  in  one  rover  and  03  per  cent,  in  the  other  rover, 
whilst  it  is  almost  8  per  cent,  in  the  ring  frame. 

The  Functioiis  of  the  Respective  Lines  of  Draw  Rollers. — There 
are  no  reasons  for  suspecting  that  the  ratios  given  in  the  last 
paragraph  differ  from  those  generally  obtaining.  Those  results 
imply  that  the  functions  of  the  middle  and  back  top  rollers 
are,  first,  that  of  obtaining  a  uniform  tension  in  that  portion 


154 


COTTON  SPINNING   CALCULATIONS 


of  the  rove  between  them ;  second,  that  of  controlhng  the  body 
of  fibres  not  within  the  nip  of  the  front  pair  of  rollers.  If 
these  inferences  are  true,  it  cannot  be  an  advantage  to  place 
the  middle  and  back  rollers  widely  apart,  also  in  having  a 
draft  greater  than  that  which  covers  the  possible  variations  in 
tension  and  natural  elasticity  of  the  rove.  For  these  reasons 
the  draft  between  the  first  and  second  lines  of  rollers  should 
always  be  low  and  in  accordance  with  the  last-named 
conditions.  The  difference  in  the  condition  in  which  the 
cotton  is  presented  in  the  slubber,  accounts  for  the  almost 
complete  realization  of  the  draft  between  the  first  and  second 
lines  of  rollers  in  that  machine. 


Front  rollep 


Hank  Indicators. 

Figs.  30  and  31  contain  the  gear  common  in  the  old  and  new 
types  of  hank  indicators  used  in  drawing,  fly,  and  ring  frames. 

In  Fig.  30  the  dial  is  numbered  from  0  to  100,  and  this  part 
is   connected   with   the   front   roller  by  the  following  train  of 

wheels :  A  single  worm 
on  the  front  roller  drives 
a  worm  wheel  of  51  teeth, 
the  subsequent  gear  being 
„      .      ^      -    drivers  ,, 

.6_    _5      _5 .      •!_    thp 

6o»  60»  60»  60'  (Jriven' 
latter  denominator  being 
the  dial  wheel. 

This  form  of  indicator 
does  not  admit  of  reliable 
fractional  readings,  and 
for  this  reason  is  being 
discarded. 

The  above  gear  is 
only  applicable  to  frames  containing  a  front  roller  1^  inch  in 
diameter. 

An  allowance  of  2|  per  cent,  is  always  made  for  breakages, 
so  that  the  indicator  registers  2^  per  cent,  less  than  the  actual 
length  delivered. 


Fig.  30. 


AND   COSTS   OF   YARN 


155 


111  the   present   instance   the    actual   length   delivered   per 
100  hanks  registered  would  be — 


GO  X  GO  X  60  X  GO  x  51  x  Ij,  x  22  X     1 
5X5    x5xGxlx36x7x840 


=  103-04 


This  is  equal  to  an  allowance  of  2"95  per  cent. 

The  particulars  of  the  size  of  roller  and  of  the  gear  are  now 
stamped  upon  each  indicator. 

ExiCRCiSE  1. — Assuming  the  other  gear  as  above,  what  size  of  worm  wheel 
would  be  suitable  for  1  J,  If,  and  1^  inch  in  diameters  of  rollers  ?     Ans.  46, 41,  38. 

Exercise  2. — What  lengths,  in  hanks,  would  be  delivered  per  100  indicated, 
if  the  indicators  used  in  frames,  containing  front  rollers  f,  1,  1},  If,  and  1.^  inch 
in  diameter,  were  geared  as  in  Fig.  30,  with  the  exception  of  the  worm  wheels, 
these  latter  being  65,  57,  46,  41,  38,  respectivety  ? 

Ans.  102,  102-5,  103,  100-9,  102-3. 

ExERCisK  3. — What  weight  would  be  produced  in  10  hours  per  frame  of  186 
spindles  if  9-4  hanks  are  recorded  and  the  count  of  the  rove  is  3-5  ?    Ans.  500  lbs. 

Exercise  4. — At  what  rate  would  it  be  necessary  to  run  the  spindles  per 
minute,  if  the  loss  of  time,  including  doffing,  was  5  per  cent.,  tlie  twist  per 
inch  2-2,  and  the  count  3i,  in  order  to  register  on  the  indicator  9-4  hanks  in 
10  hours?  "  ^«s.  1125. 

In  Fig.  31  there  are  three  index  discs,  that  on  the  left  hand 
recording  tens,  that  in  the  centre  the  units,  and  that  on  the 
right  hand  the  decimals,  each 
disc  being  numbered  from  1  to 
10  and  each  free  upon  the 
central  spindle.  The  driving 
from  the  front  roller  is  by  a 
worm  driving  the  36,  and  thence 
to  the  decimal  dial  wheel :  the 


gear  is 


•2  4 


_^8 
2  0' 


The  units 


dial  is  driven  from  the  decimal 
dial  by  a  train  ^  X  .f^y,  and  the 
tens  dial  is  driven  from  the  latter  by 


Fig 


2  0" 


Thus  the  calculated  length  delivered  per  100  recorded- 
20x4x20x4  X  20x4x24  X36x9x22x  1  X   1 


~  8x1x8x1x8x1x1  Xl  X8X7X36X840 
=  101  hanks 


156  COTTON   SPINNING   CALCULATIONS 

Exercise  5. — What  length  iu  hanks  would  be  delivered  per  100  recorded  if 
the  36  worm  wheel  is  changed  to  37  ?  Ans.  103-8. 

Exercise  6. — What  length  in  hanks  would  be  delivered  per  100  recorded  if 
the  36  and  34  worm  wheels  are  changed  to  35  and  25?  Ans.  102*3. 

Exercise  7. — What  w^eight  of  4'  roving  will  be  produced  in  a  frame 
containing  200  spindles  per  52  hanks  recorded  by  an  indicator,  as  in  Fig.  31, 
assuming  the  loss  is  actually  2i  per  cent.  ?  Ans.  2560  lbs. 

Length  or  Full  Bobbin  Stop  Motions. 

Fig.  32  represents  a  length  stop  motion  applicable  in  fine 

work  when  a  number  of  sets  of  bobbins  are  required  containing 

exactly  the  same  length.     This  motion  is  very 

^"i^^  c  1  °^^°     convenient  in  the  preparation  of  special  rove 

I-— H-      ni     for  spinning  samples  and  small  quantities,  and 

O      P"i  In      "when  not  more  than  the  roving  necessary  to 

make  the  yarn  is  required. 

A  is  a  worm  on  the  front  roller,  B  a  worm 

Fig.  32.  wheel,  C  a  worm  on  the  latter,  driving  D,  D  is 

compounded  with   the  worm  E  ;    E  drives  F, 

and  this  is  attached  to  a  peg  disc  G ;  a  suspended  catch  H 

operates  the  strap  control  release  bar  I  at  each  revolution  of  G. 

B  is  the  change  wheel. 

The  length  of  roving  delivered  per  action  of  this  motion  with 

the  front  roller  1'  inch  in  diameter  =  ^  X  ^^  X  ^-  X  ^^4^ 

1  1  1  do 

=  4295  yards. 

Exercise  1. — What  size  of  change  wheel  (35)  would  be  required  to  make 
bobbins  containing  21  leas,  73  yards?  Ans.  27. 

Exercise  2. — A  roving  frame  containing  200  spindles  is  required  to  prepare 
500  lbs.  of  20'  roving  for  a  mule  using  double  roving  and  containing  1000  spindles. 
What  change  wheel  will  give  the  nearest  approach  to  the  necessary  length  on 
each  bobbin  ?  Ans.  34. 

Exercise  3. — What  lengths  of  roving  will  be  delivered  by  the  front  roller 
per  action  of  this  part  with  change  wheels  ranging  from  25  to  45  respectively  ? 


Mule  Calculations. 

The  Gearing  in  Mules. — The  parts  engaged  during  spinning 
receive  their  motion  from  the  rim  shaft.- 

Those  parts  that  are  engaged  whilst  spinning  is  in  abeyance 


AND   COSTS   OF   YARN  157 

receive  their  motion  through  the  shaft  designated  the  backing- 
oflf  and  taking-up  motions  shaft. 

The  rim  and  the  backing-off  and  taking-up  motions  shaft 
receive  their  movement  from  the  line  shaft,  usually  through  the 
medium  of  a  counter  shaft.  This  system  of  driving  obtains 
better  control  than  when  driven  direct  from  the  line  shaft. 

The  draft  gear  in  these  machines  is  identical  with  that  in 
the  fly,  and  ring  frames.  Eeference  to  those  will  make  clear  all 
that  can  be  said  respecting  drafts  and  changes  in  the  counts  in 
mules.    Examples  are  given  later  in  this  section. 

(a)  The  spindles  are  connected  with  the  rim  shaft  by  an 
indirect  train,  comprising  two  direct  trains  of  pulleys  and  bands, 
the  rope  from  the  pulley  on  the  rim  shaft  being  guided  to  one 
on  the  tin  roller  shaft  by  suitable  carriers.  The  last-named 
shaft  is  coupled  to  a  series  of  long  drums  known  as  tin  rollers, 
these  drive  bands  conveying  the  motion  to  grooved  pulleys  or 
wharves  on  the  spindles.  The  rim  pulley  is  the  usual  change 
part  in  this  train.  In  some  makes  slight  changes  are  also 
arranged  for,  in  the  size  of  the  tin  roller  pulley  ;  it  is  then  made 
in  two  detachable  portions.  When  a  change  in  the  speed  of  the 
spindle  is  expedient,  this  change  is  used  for  altering  the  rate  of 
rotation  of  the  spindle  and  its  relation  with  other  parts. 

(b)  The  connecting  gear  from  the  rim  shaft  to  the  front  roller, 
in  most  makes  of  mules,  consists  of  an  indirect  train  of  six  wheels, 
arranged  in  three  direct  or  simple  trains.  These  are  conveniently 
mounted  to  enable  at  least  one  driver  and  one  driven  wheel  to 
be  changed.  A  change  in  the  value  of  this  train  is  necessary 
when  an  alteration  in  the  relation  of  the  rollers  with  the  rim 
shaft  is  required.  Also,  when  a  change  in  the  speed  of  the 
spindle  is  desired,  but  without  any  alteration  in  the  relation 
between  this  part  and  the  rollers. 

(e)  The  front  roller  is  connected  with  the  back  roller  by  an 
indirect  train  of  four  wheels  comprising  two  direct  trains.  These 
wheels  are  named  the  draft  wheels  and,  respectively,  the  front 
roller,  crown,  pinion,  and  back  roller  wheels.  The  two  latter 
are  conveniently  mounted  for  changing,  being  the  medium  of 
alterations  in  the  draft. 

The   middle   back  rollers  are  connected  by  a  direct   train. 


158  COTTON   SPINXIXG  CALCULATIONS 

comprising  three  wheels,  in  the  same  manner  as  in  fly 
frames. 

((/)  The  carriage,  of  spindles,  is  drawn  outward  by  two  sets 
of  ropes  attached  to  drums  secured  upon  the  back  shaft.  The 
latter  being  connected  with  the  front  rollers  by  an  indirect  train 
of  five  wheels,  these  comprise  two  direct  trains.  Those  wheels 
are  conveniently  arranged  to  enable  a  driven  and  a  driver  to  be 
changed.  They  are  known  as  the  gain  and  gain  boss  wheels 
respectively,  the  last  named  driving  the  wheel  on  the  back 
shaft.  These  wheels  are  the  medium  of  alterations  in  the  rate 
of  movement  of  the  carriage,  relative  to  that  of  the  front  roller  ; 
and  therefore  they  control  the  tension  in  the  yarn  during 
spinning.  In  spinning  the  poorer  classes  of  yarn  gain  is  often 
a  minus  quantity.  The  "jacking,"  "  ratching,"  or  stretching 
motion  is  the  means  by  which  yarns  may  be  improved,  during 
spinning,  by  the  elimination  of  soft  thick  portions.  The  motion 
is  not  usually  adopted  for  other  than  fine  work,  because  it 
reduces  the  production  considerably,  thereby  increasing  the  cost 
of  spinning.  It  is  the  medium  for  actuating  the  backshaft  train 
at  }  to  I  the  normal  rate,  and  during  this  action  the  rollers  are 
either  at  rest  or  moving  at  an  almost  imperceptible  rate.  This 
action  has  the  effect  of  moving  the  carriage  at  from  ^  to  I  of  the 
normal  speed,  and  hence  the  yarn  is  stretched  and  made  more 
uniform  by  the  thicker  portions  being  attenuated.  In  accom- 
plishing this  successfully  it  is  necessary  that  the  3'arn  should 
only  receive  a  portion  of  its  twist  prior  to  this  action.  The 
exact  amount  cannot  be  stated,  because  it  varies  in  extent,  with 
the  circumstances,  from  -^  to  |  of  that  required,  being  lowest  in 
the  best-prepared  and  long-stapled  cottons.  When  the  com- 
pleted yarn  contains  above  the  standard  twist,  much  twisting  is 
necessary  "at  the  head."  This,  if  completed  at  the  ordinary 
speed  of  the  spindle,  results  in  a  considerable  loss  of  time. 
The  gearing,  comprised  in  this  motion,  varies  in  the  different 
makes.     Three  types  are  contained  in  Figs.  34,  36,  37,  and  38. 

(e)  The  slow  roller  turning,  or  "  receding,"  motion,  contained 
in  Figs.  34  and  36,  consists  of  a  train  of  wheels  in  uninterrupted 
connection  with  the  rim  shaft.  This  prevents  the  front  roller 
from  being  at   rest  whilst  the  rim  shaft   is   rotating    in    the 


AND   COSTS   OF   YARN  159 

"twisting"  direction.  Tiiis  action  eliminates  the  tendency  of 
**  twisting  down  "  of  the  ends  during  jacking.  It  is  constructed 
with  an  escapement  allowing  the  front  roller  to  be  driven  by 
the  major  movement  active. 

The  twisting  motion,  shown  in  Figs.  34  and  36,  controls  the 
twist.  It  is  only  used  in  those  mules  wherein  the  twist  cannot 
be,  advantageously,  completely  inserted  whilst  the  carriage  is 
moving,  necessitating  the  completion  of  twisting  with  the 
carriage  at  rest  at  the  "head."  This  motion  controls  the  rim 
shaft  driving  strap.  The  mechanism  consists  of  a  detent  catch 
for  holding  the  strap  fork  lever,  this  is  released  by  a  "  tumbler" 
operated  by  a  train  of  wheels  that  are  in  connection  with  the  rim 
shaft.  One  or  two  of  these  wheels  are  mounted  conveniently  for 
changing.  These  change  wheels  are  termed  the  twist  wheels 
because  they  control  the  revolutions  which  the  rim  and  the  tin 
roller  shaft  and  the  spindles  make  per  draw,  and  thus  the  twist 
inserted  in  the  yarn. 

The  double  speed  motion,  for  rotating  the  spindles  at  two 
different  rates,  aims  at  the  reduction  of  the  time  occupied  in 
spinning,  when  "jacking  "  is  in  vogue,  by  actuating  the  spindles 
at  the  maximum  rate  throughout.  Prior  to  jacking,  the  speed 
of  the  spindles  must  be  in  accordance  with  the  resistance  of  the 
yarn.  As  the  degree  of  twist  increases  and  improves  the  strength 
of  the  yarn,  the  spindles  are  rotated  at  a  higher  speed,  some- 
times almost  double  the  former  rate.  For  this  work  two  drums 
of  different  sizes  may  be  employed,  to  drive  the  counter  shaft 
alternately,  as  shown  in  Fig.  35. 

Two  different  sizes  of  rims  separately  driven  are  also  used 
for  the  same  purpose. 

The  building  motion  consists  of  a  mechanism  for  raising  the 
range  of  movement  of  the  directing  faller  wire  so  that  the  yarn 
is  laid  in  layers,  progressively  ascending,  upon  the  spindle.  The 
rate  of  this  movement  determines  the  thickness  of  the  body  of 
yarn  so  formed,  and  therefore  that  of  the  cop.  The  parts 
actuating  this  movement  are  :  a  screw,  which  operates  the  with- 
drawal of  the  inclined  plates  supporting  the  copping  rail, 
having  a  ratchet  wheel  secured  to  it — the  latter  being  actuated, 
by  the  passage  of  a  curved  or  inclined  bracket  secured  to  the 


160  COTTON   SPINNING  CALCULATIONS 

carriage  front ;  an  adjustable  number  of  teeth  per  draw,  through 
the  medium  of  a  pawl  and  pawl  lever.  The  pawl  lever,  at 
each  passage,  is  pushed  prior  to  the  termination  of  each  outward 
movement  of  the  carriage.  The  extent  of  this  movement  is 
adjusted  by  varying  the  inclination  of  the  curved  bracket,  and 
also,  by  the  use  of  screws  of  difterent  pitch.  Eatchet  wheels  are 
made  a  standard  diameter  by  each  maker,  but  with  varying 
numbers  of  teeth.  Whenever  convenient  the  wheel  is  moved 
one  tooth  per  draw  only. 

The  Roller  Delivery  Motion,  during  Winding. — This  motion 
usually  consists  of  a  direct  train,  composed  of  three  wheels,  for 
driving  the  front  rollers  during  the  inward  run  of  the  carriage. 
This  is  effected  from  the  back  shaft.  The  wheel  on  the  latter, 
or  that  on  the  front  roller,  is  furnished  with  an  escapement  that 
allows  of  the  front  roller  being  driven  by  the  major  movement 
active. 

The  winding  motion  is  similar  in  construction  in  all  the 
types  of  mules  in  general  use.  It  consists  of  an  actuating 
chain  and  chain  barrel,  with  a  direct  train  connection  to  a  wheel 
on  the  tin  roller  shaft.  This  generally  consists  of  two  wheels, 
one  of  these  communicating  the  movement  to  the  shaft  through 
an  escaj^ement  that  allows  the  tin  roller  to  be  always  under  the 
influence  of  the  major  movement.  The  rate  at  which  the  chain 
is  unwound  from  the  barrel  controls  the  spindle.  The  rate  of 
the  unwinding  of  the  chain  is  determined  by  the  radius  described 
by  the  other  end  of  the  chain.  This  is  secured  to  a  nut  on  a 
screw  within  the  quadrant  arm,  the  screw  being  actuated  in  one 
direction  only,  and  this  increases  the  radius  described  by  the  nut. 
This  is  the  function  of  the  automatic  winder  governing  motion. 

The  backing-off  and  taking-in  motion  is  shown  in  each  of  the 
Figs.  33  and  34.  This  is  the  same  in  all  types  of  mules  except 
that  the  value  of  the  train  and  rate  of  movement  are  varied. 

During  recent  years  considerable  improvement  has  been 
made  in  this  motion.  The  change  enables  the  tension,  to 
which  the  yarn  is  subjected,  to  be  adjusted  in  the  most  desirable 
degree.  This  is  obtained  by  the  introduction  of  parts  which 
control  the  engagement  of  the  backing-off  friction,  and  allow  this 
to  be  deferred  until  the  momentum  of  the  rim  shaft  is  reduced  to 


AND   COSTS  OF  YAKN  161 

the  desired  degree.  The  effects  are  that  backing-off  frictions 
may  be  run  at  slower  rates  and  are  more  reliable.  They  can  be 
adjusted  more  definitely  to  the  requirements. 

The  Hastening  Motion. — The  usefulness  of  self-acting  mules 
for  the  finest  counts  has  been  improved  by  the  introduction 
of  figure  35  type  of  this  motion.  Its  aims  are  to  secure  the 
desired  adjustment  in  the  number  and  spacing  of  the  coils 
wound  upon  the  spindle  at  the  termination  of  winding.  Also, 
to  relieve  thereby  the  strain  upon  the  yarn  during  the  action 
of  bacldng-off. 

Twist. — The  following  are  the  common  twist  constants' 
standards  in  connection  with  the  ordinary  qualities  of  single 
yarns  : — 

Descriptiou  of  the  V  count  x  constant 

cotton  and  yarn.  =  twist  per  inch. 

Egyptian  weft 3-18 

American    „ 3'25 

Doubling     „       3-49 

American  twist 3*75 

Egyptian      „ 3-606 

Ring  „ 4-0 

The  Conditions  governing  the  Various  Changes  in  the  Wheel 
Train  Values  in  Mules. — (1)  The  speed  of  the  spindle  should  be 
the  highest  consistent  with  the  quality  of  yarn  required,  and  with 
due  regard  to  the  wear  and  tear  of  the  machine.  The  rim  pulley 
is  the  medium  of  alteration. 

(2)  The  twist  required  in  the  yarn  must  conform  with  the 
standards  given  above.  This  controls  the  sizes  of  the  rims, 
twist  and  speed  wheels.  « 

(3)  The  most  beneficial  rate  at  which  the  carriage  may  be 
moved  outward  often  restricts  the  speed  at  which  the  spindles 
run,  and  determines  the  size  of  the  speed  wheel.  Five  draws 
in  60  seconds  is  considered  the  maximum  rate  at  which  the 
carriage  may  be  worked. 

(4)  The  count  of  the  roving  available  and  that  of  the  yarn 
desired. 

(5)  The  "gain"  or  ''drag"  must  be  governed  by  circum- 
stances ;  generally  it  is  beneficial  in  attenuating  the  thick  soft 
and  breaking  the  weak  parts  of  the  yarn.    At  the  same  time  it 

M 


162  COTTON   SPINNING   CALCULATIONS 

eliminates  snarls,  and  is  usually  applied  to  the  greatest  extent 
practicable.  This  governs  the  relation  between  the  movement 
of  the  carriage  and  rollers. 

(6)  "Jacking"  or  "ratch"  can  only  be  adopted  when  time 
and  other  circumstances  permit.  Generally  it  is  only  adopted 
to  a  very  limited  extent  in  other  sections  than  the  production  of 
fine  yarns.  It  is  essential  in  the  production  of  yarns  of  a 
superior  quality ;  sometimes  it  is  applied  to  the  extent  of  as 
much  as  4^  inches  in  a  draw  of  60  inches. 

(7)  The  "  shaper"  wheel  governs  the  thickness  of  the  cop. 
In  changing,  the  following  precautions  should  be  noted  : — 

(1)  Avoid  changing  the  twist  by  means  of  either  the  speed  wheel 
or  rim  pulley  before  ascertaining  whether  a  change  in  the 
spindle  or  carriage  speed  will  be  most  beneficial,  and  to  what 
extent  each  of  these  may  be  altered  to  advantage. 

(2)  Before  changing  the  twist  wheel,  consider  whether  the 
proposed  alteration  can  be  accomplished  to  greater  advantage  by 
means  of  the  rim  or  speed  wheel. 

(3)  Always  notice  and  collect  data  of  the  difference  between 
the  calculated  and  actual  results.  These  vary  very  considerably 
in  the  non-positive  gear,  and  can  only  be  satisfactorily  deter- 
mined in  this  way. 

(4)  Check  the  accuracy  of  the  effects  of  the  draft.  This  is 
readily  done  at  the  spindle  point  by  taking  a  sufficient  number  of 
ends,  of  a  standard  length,  to  enable  the  counts  to  be  ascertained. 

(5)  The  differences  in  the  rate  of  spindles  vary  very  much, 
and  in  ascertaining  the  actual  twist,  several  tests  should  be  made. 

Calculations  and  other  Particulars  of  the  Various 
Trains  of  Gearing. 

Fig.  33  is  a  plan  of  the  gearing  as  found  in  the  Hetherington 
mule  for  coarse  and  medium  counts-  The  particulars  relating  to 
the  driving  of  the  rim  shaft  in  this  figure  are — 

Line  shaft,  235  revolutions  per  minute ;  diameter  of  drum, 
32  inches. 

Counter  shaft :  fast  and  loose  pulleys,  16  inches ;  driving 
drum,  28  inches  diameters. 


AND   COSTS   OF   YARN 


163 


Revolutions  of  tlic  rim  shaft  jX'V  minute — 
235  X  32  X  28 


16  X  14 


=  940 


(a)  Revolutions  of  the  spindles  per  minute,  when  the  rim  pulley 
is  12  inches  and  the  tin  roller  pulley  12  inches — 


940  X  12  X  6 
12  X  5 


=  7520 


50 
Taking  in 
^?7^shaft  2f  revs. 

per  draw 
75 

Back  Shaft 
3rrevs.=  64' 


10/ 


Fig.  33. 

Therefore,  the  different  speeds  of  the   spindles   obtainable 
by  the  range  in  the  sizes  of  rims  (12  to  22  inches)  are  = 

13"        14"        15"       16"       17" 


Size  of  rim 12" 

SizeofT.KP 12" 

Revs,  of  spindle  per  miu.       7520 


8150      8780      9420    10,050    10,080 


164  COTTON   SPINNING   CALCULATIONS 

Size  of  rim 18"         19"         20"         21"         22" 

Size  of  T.E.P 12" 

Kevs.  of  spindle  per  min.    11,300    11,730    12,530    12,970    13,600 

2sfoTE. The  actual  will  differ  considerably  from  the  calculated  speed.     The 

loss  between  the  rim  shaft  and  the  spindle  will  be  from  5  per  cent,  upwards, 
when  the  diameters  of  the  surfaces  in  the  train  are  measured  in  the  customary 
way. 

(h)  The  rate  of  rotation  of  the  front  roller  relative  to  the 
spindles  is  varied  in  order  to  obtain  the  desired  twist.  The  train 
connecting  the  front  roller  with  the  rim  shaft  is  provided  with 
suitable  change  gear  for  that  purpose.  The  length  delivered  by 
the  front  roller  during  the  outward  run  of  the  carriage,  varies 
with  the  amount  that  the  latter  is  desired  to  *'gain."  The 
movement  by  the  carriage  is  from  68  inches  to  58|  inches,  the 
former  in  mules  for  coarse,  and  the  latter  in  those  for  fine,  work. 
Assuming  no  "  gain,"  the  surface  rates  of  the  movement  of  the 
rollers  and  carriage  correspond.  Thus,  with  the  front  roller 
1  inch  in  diameter  and  the  draw  64  inches,  the  front  roller 
makes — 

-jj — 22"  =  2^A  revolutions  per  draw 

With  the  gearing  from  the  rim  shaft  to  the  rollers  arranged 
to  give  the  quickest  movement  practicable  within  the  range  of 
change  wheels  stated :  the  largest  driver  and  the  smallest  driven 
change  wheels  must  be  adopted ;  whilst  in  the  train  from  the 
rim  shaft  to  the  spindles,  the  smallest  drivers  and  the  largest 
driven  change  wheels  are  necessary.  Thus,  neglecting  the 
slippage  arising  in  respect  of  the  connection  to  the  spindles,  the 
revolutions  of  the  spindle  per  20 1\  revolutions  of  the  front 
roller  would  be — 

20  4   X  38  X  35  X  40  X  12  X  6  ^ 

"^^11  ^  20  X  35  X  30  X  12  X  I 

This  represents  the  least  twist  per  draw  under  the 
conditions  named, 

412*5 
The  twist  per  inch  of  yarn  is  therefore  ^^^  =  6*44. 

Thus,  driver  wheels  and  driven  pulleys  in  this  connection 


29 

28 

27 

26 

25 

24 

426 

441 

457 

475 

494 

515 

6-66 

0-88 

7-14 

7-43 

7-82 

8-05 

22 

21 

20 

19 

18 

17 

562 

588 

618 

650 

687 

728 

AND   COSTS   OF   YARN  165 

reduce  the  twist  inversely  to  changes  in  their  size,  whilst  driven 
wheels  and  driver  pullej's  have  the  inverse  effect.  Therefore, 
the  revolutions  of  the  spindles  per  draw  and  the  twist  inserted 
per  inch  of  yarn  spun,  with  other  change  wheels  than  those 
given  in  the  previous  calculations,  are  as  follows  : — 

(pi)  Size  of  wheel  on  the  rim  shaft  .  30 
Eevs.  of  spindle  per  draw  .  .  412 
Twist  per  inch 6-44 

Size  of  wheel  on  the  rim  shaft  .  23 
Revs,  of  spindle  per  draw  .  .  537 
Twist  per  inch 8-4   8-78     9-2    9-66   10-15    10-7    11-37 

The  revolutions  of  the  spindles  per  draw  possible  with  the 
range  in  speed-wheels  (40-60),  as  specified,  and  the  rest  of  the 
speed  gear,  excepting  that  a  wheel  of  17  teeth  replaces  the  30 
on  the  rim  shaft,  as  given  in  the  previous  calculation,  are  as 
follows  : — The  train   from  the   rollers  to  the  rim  shaft  when 

Of.  y.  Q" Tw  obtains  728  revolutions  of  the  spindle  per  draw 

of  20/^-  revolutions  of  the  front  roller.  The  40  in  this  train 
is  the  speed  wheel  and  therefore  increasing  the  size  of  this 
will  cause  a  reduced  rate  of  movement,  by  the  rollers  and 
carriage,  inversely  to  the  change  in  these  wheels,  and  hence 
proportionately  more  twist  in  the  following  amounts  : — 

(6,)  Size  of  speed  wheel    .    .     40      41     42     43   ...    50  ...    55    ...    60 
Revs,  of  spindle  per  draw    728    746    764    782  ..  .   910  ..  .  1002  .  .  .  1092 
Twist  per  inch  ....  11-37  11-6  11-9  12-2  .  .  .  14-2  .  .  .  15-6  ...      17 

FurLher  increases  in  the  twist  may  be  obtained  by  increasing 
the  value  of  this  train.  This  may  be  accomplished  by  reducing 
the  number  of  the  teeth  contained  in  the  wheel  on  the  same 
axis  as  the  speed  wheel  (35),  and  also  the  bevel  wheel  (20), 
driving  that  on  the  front  roller  shaft.  The  latter  is  named  the 
front  roller  clutch  bevel.  By  replacing  these  with  27  and  17 
respectively,  the  range  of  twist  obtainable  when  a  60-speed 
wheel  is  also  employed,  becomes — 

4  38  X  35  X  60  X  12  X  6  ^  ( 1670  revolutions  of  twist  per 
^^  1       17  X  27  X  17  X  12  X  ^      (      draw 


45  .  . 

.  50  .  , 

,  .  55  .  . 

,  .  60 

1250  .  . 

.  .  1390  .  . 

,  .  1530  .  . 

.  1670 

195  .  . 

.  21-6  .  . 

.  23-8  .  . 

.  26-1 

166  COTTON   SPINNING  CALCULATIONS 

Thus :  when  the  speed  wheel  is  altered  to  40  the  twist  per 
draw  becomes — 

„„  4    ^  38  X  35  X  40  X  12  X  6      ...^ 
^'       17  X  27  X  17  X  12  X  ^ 

Hence,  the  revolutions  of  the  spindles  per  draw  and  the 
twist  per  inch  obtainable  by  using  the  various  sizes  of  speed 
wheels  comprised  in  the  range  will  be — 

(Jg)  Size  of  speed  wheel     .     .    40 
Revs,  of  spindle  per  draw  1112 
Twist  per  inch  ....  17-3 

Assuming  that,  after  the  above-stated  changes,  the  range  in 
the  sizes  of  the  speed  change  wheels  exhausted,  further  altera- 
tion in  the  twist  would  only  be  practicable  by  changes  in  the 
train  of  rope  and  band  driving  gear,  from  the  rim  shaft  to 
the  spindles.  Such  would,  at  the  same  time,  alter  the  speed 
of  the  spindles  as  per  paragraph  (a).  The  changes  in  twist 
obtainable  with  the  range  in  sizes  of  rim  pulleys  available,  as 
specified,  are — 

Size  of  rim  in  inches 
Twist  per  inch  with  the  \  40 
appended  speed  wheels  )  60 

Size  of  rim  in  inches 

Twist  per  inch  with  the?  40  =  24-5 

appended  speed  wheels  i  60 

Basis  64  inches  =  draw. 

It  is  customary,  also,  to  make  the  tin  roller  pulley  in  halves 
in  order  to  admit  of  its  being  changed  :  the  range  is  from 
10  inches  to  12  inches.  In  the  present  instance  the  latter  is  in 
use.  Altering  this  would  affect  the  twist  and  at  the  same  time 
the  speed  of  the  spindles  in  the  inverse  proportion. 

(c)  "  Gain"  Changes. — The  back  shaft,  in  pulling  out  the  car- 
riage, is  assumed  to  make  a  fixed  movement.  This  is  not  exactly 
the  case,  because  this  movement  must  be  subject  to  variations 
arising  through  differences  in  the  tension  of  the  ropes  and 
matters  influencing  the  resistance  to  the  movement  of  the 
carriage.     For  the  purpose  of  calculation  it  is  convenient  to 


12 

13 

14 

15 

16 

17-3 

18-7 

20-2 

21-6 

23-0 

26-1 

28-3 

30-5 

32-6 

34-8 

17 

18 

19 

20 

24-5 

25-9 

27-4 

28-8 

37  0 

39-2 

4L-4 

43-5 

AND  COSTS  OF  YAKN  167 

make  the  assumption  named.  In  the  present  instance,  the 
movement  of  the  back  shaft  is  taken  at  3g  revolutions  per  draw, 
so  that  with  the  smallest  gain  boss  (25-27)  and  gain  wheels 
(97-112),  and  with  the  rest  of  the  connecting  gear  from  the  front 
roller  to  the  back  shaft  as  specified,  the  length  delivered  by 
the  front  roller  during  this  movement  would  be — 

S^  X '^--^-  =  I  "'•''' '^^     ^revolutions     of     the 
^      25  X  60  front  roller  per  draw 

and  therefore  17'46  x  1  x  ^-  =  54-87  inches  delivered 

With    the    following   **gain"   change    wheels,   the    length 
delivered  by  the  front  roller  and  the  *'  gain  "  would  be  : — 

Gain  wheel 97  98  99  100  101  102 

Gain  boss  wheel 25  25  25         25  25  25 

Inches  delivered  by  rollers  per  draw  5i-87  55-5  56-0  56-6  57-2  57-7 

Gain  in  inches 9-13  8-5  8-0        7*4  6-8  6-3 

Gain  wheel 103  104  105  106  107  108  109 

Gain  boss  wheel 25       25  25  25  25  25       25 

Inches  delivered  by  rollers  per  draw  58-3  58-8  59-4  60-0  60-G  GM  61-7 

Gain  in  inches 57  5-2  4*6  4-0  3-4  2-9  2-3 

Gain  wheel 110  111  112  112  111  110 

Gain  boss  wheel 25  25         25  26  26  26 

Inches  delivered  by  rollers  per  draw  62-3  62-8  63-4  60-9  60-3  59-8 

Gain  in  inches 1-7  1-2  0-6  3*1  37  4-2 

Gain  wheel 109  ...  112  111  110  109  ..  . 

Gain  boss  wheel 26  ...  27  27  27  27  .  .  . 

Inches  deHvered  by  rollers  per  draw  593  .  .  .  587  58-2  577  57-1  .  .  . 

Gain  in  inches 47  ...  5-3  5-8  6-3  6-9  ... 

The  changes  in  the  length  delivered  by  the  front  roller  per 
draw  during  the  outward  run  of  the  carriage,  is  directly  pro- 
portionate to  the  changes  in  the  size  of  gain,  and  inversely  in 
respect  of  the  gain  boss,  wheels. 

Yarns  highly  twisted  and  of  poor  quality  do  not  admit  of  the 
carriage  gaining  on  the  rollers.  In  such,  the  rollers  more  fre- 
quently deliver  at  a  rate  in  excess  of  that  moved  by  the  carriage. 
This  is  sometimes  as  much  as  10  per  cent.  In  the  production 
of  the  best  qualities  of  yarn,  when  fully  twisted  as  the  carriage 
moves  out,  only  a  slight   "  gain  "  is   practicable.     *'  Gain  "  is 


168  COTTOK   SPINNING  CALCULATIONS 

most  applicable  with  low  spindle  speeds  and  when  the  yarns  are 
not  fully  twisted  during  the  movement  of  the  carriage. 

Changes  in  the  Builder  Wheel. — The  approximate  size  of  suit- 
able builder  wheel,  may  be  ascertained  as  follows,  when  the  size 
of  cop  required  is  known  : — 

-J-  =  suitable  builder  wheel 
dc 

b  =  the  length  in  inches  of  the  yarn  contained  in  the  cop. 

d  =  tJie  length  wound  in  inches  per  draw. 

c  =  the  revolutions  of  the  copping  screw  necessary  in 
completing  the  cop. 

h,  is  ascertained  from  the  weight  of  the  cop  in  grains, 
divided  by  the  weight  of  one  hank  in  grains,  and  multiplied  by 
the  inches  per  hank.     Thus — 

nettTveishtrf^cop  in  grains  ^  g^^  ^  gg  ^^ 

count 

c,  is  ascertained  by  marking  upon  the  spindle  the  length 
which  the  cop  measures,  from  the  cop  bottom  to  the  bottom  of 
the  chase;  and  then  proceeding  to  turn  the  copping  screw 
sufficient  to  pass  the  winding  faller  wire  through  the  movement 
marked  on  the  spindle,  opposite.  This  must  be  done  whilst  the 
carriage  is  at  rest,  with  the  trail  lever  bowl  on  the  ridge  of  the 
copping  rail,  and  the  revolutions  of  the  screw  counted. 

Ascertaining  the  Suitable  Builder  Wheel  in  changing  Counts. — 
Changing  the  counts  affect  the  weight  of  the  cops  in  the  inverse 
proportions,  and,  assuming  the  tension  of  the  yarn  during 
winding  proportional  to  the  area  of  the  yarn,  the  diameter  of 
the  cop  would  be  affected  in  the  inverse  proportion  to  the 
^/counts.  Thus,  the  mode  of  calculating  this  wheel,  in  order  to 
obtain  a  cop  of  constant  size,  should  be  as  follows  : — 

Present  wheel  X  ^required  count  ^  ^^^^.^,^^  ^^^^^ 
^/present  count 

Note. — A  difference  in  the  size  of  the  cop  must  alwaj's  result  when  the  yarn 
is  wound  at  other  tension  than  inversely  proportional  to  the  difference  in  the  area 


AND   COSTS   OF  YARN  169 

of  the  yarn.  Also,  when  (lie  change  alters  the  quality  of  the  yarn  in  any  way, 
the  difficulty  of  adjusting  the  tension  in  the  correct  order  is  such  that  the  above 
rule  cannot  be  relied  upon.  The  following  rule  will  be  found  more  reliable  but 
must  not  be  regarded  as  accurate  in  all  cases  : —  ' 

Required  wheel  =  Pi'esent  wh^Vrequired^ount _^ present  wheel  x  required  count 
2v'present  count  2  x  present  count 

Ascertaining  the  suitable  builder  wheel  in  changing  the  size  of  the  cops 
only —  ^ ' 

Present  wheel  (diameter  of  required  cop)2 
(diameter  of  present  cop)^ 

The  following  are  exercises  in  calculating  the  alterations 
necessary  to  adapt  the  gearing  in  Fig.  33  for  the  work  given. 
They  are  given  in  tabulated  form  because  it  is  more  convenient 
Allow  10  per  cent,  for  slippage  in  the  driving  of  the  spindles 
from  the  rim  shaft,  and  use  the  customary  twist  constants  where 
the  twist  is  not  given. 

Explanation  of  the  tahulated  exerdscs.—llho^Q  columns 
numbered  1  to  16  are  separate  exercises.  The  data  required 
is  signified  by  (?).  Base  the  calculations  for  the  builder  wheel 
on  that  given  in  Exercise  1.  The  items  referred  to  in  each 
column  are  contained  opposite  in  the  first  two  columns  on  the 
left  hand. 


170 


COTTON   SPINNING  CALCULATIONS 


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AND  COSTS   OF   YARN 


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172  COTTON   SPINNING    CALCULATIONS 


Examples  in  Calculatixg  the  Exercises  on  Page  170-1. 

The  following  changes  would  be  necessary  to  adapt  the  gear  in  Fig.  33  for 
the  conditions  stated  : — 

ExEKCiSE  1. — To  drive  the  spindles  at  6000  revolutions  per  minute,  actual, 
with  a  12-inch  rim: 

The  calculated  rate  of  the  spindles  will  =  ^^^^on  ^^^  =  ^^^^  ^^^  •''  *^^^ 
Revolutions  of  Rim  Shaft. — With  the  minimum  and  maximum  sizes  of  driver 
and  driven  change  pulleys  respectively  (see  par.  (a),  p.  163)  — 

Revolutions  of  the  rim  shaft  per  minute  =  ^^^^  ^  i^]l  =  834 

6  X  12 

Speed  and  Twist  Changes. — The  front  roller,  if  1  inch  in  diameter,  and  there  is 

64"  X  7 
no  gam,  will  be  required  to  make  — ^ —  =  20i\  revolutions  per  draw.     During 

this  movement   the   spindles  are  required  to   insert  twist  to  the   extent  of 

3-75 v'S  =  10-6  per  inch,  or  3-75^8  x  64  (inches  per  draw)  =  753,  actual;  and 

therefore  the  calculated  revolutions  of  the  spindle  per  draw  are ^^ =  837, 

or  -S^j^  =  13-1  calculated  twist  per  inch. 

The  train  of  gear  connecting  the  spindle  and  the  front  roller  (see  pars,  (a),  (b), 

pp.  163-4)  must  therefore  have  the  following  value :  |^  =  ^^\^/^  =  41-1. 

According  to  the  range  in  the  change  wheels  given  in  Fig.  33  the  lowest 

,        .,,.,..    6-0  x  12  X  40  X  35  X  38      ^^  „ 

value  of  this  tram  is  ,r-^r^ ^- ^-r — -~ -—  =  20-2. 

0-75  X  12  X  30  X  35  X  20 

Hence,  altering  the  value  of  any  of  the  wheels  contained  in  this  train,  to 

increase  their  ratio  20*2  to  41-1,  will  have  the  effect  desired.     Namely,  changing 

the  twist  to  13*1  calculated. 

(driven) 

40  .  40      41-1 

Therefore  the  wheels  7.^  =  1-3  must    be    altered  in  value  to   oq  x  oKTo 

(driver) 

-  "=  '  -  20 

Therefore  the  required  wheel  on  rim  shaft  =  20,  and  the  speed  wheel  =  54. 

For  "Gain"  Wheel,  see  pp.  166-7. 

The  Draft  required  in  the  rollers  is  that  necessary  to   attenuate    11'   to 

8       16 
8'  count,  or  y^  =  -o-  =  5|.     By  assuming  the  draft  change  pinion  necessary, 

Ig  o 

X,  the  following  equation  is  obtained  : — 


54      130      1       Ki  54      130 

^  X  16   X  I  =    ^  •••  ^  =  51  ><  T6 


The  range  of  sizes  of  draft  pinion  wheels  that  can  be  accommodated  is, 
approximately,  from  30  to  60,  and  on  the  back  roller  from  40  to  60.     The  wheel 


AND  COSTS   OF  YARN  173 

82  is,  therefore,  too  large,  and  hence  it  is  necessarj'  to  reduce  the  size  to  within 

driver       82 

the  ransre  of  accommodation.     The  ratio  of  these  two  wheels  is  -r— =  i^-, 

°  driven      54 

or  1-52. 

Hence,  any  of  the   following  pairs   of  wheels  would  be   suitable  for  the 

47    56   59 
position:  31,  3--.  3C,- 

Exercise  6. — In  this  instance  the  length  of  yarn  to  be  wound  each  draw 
is  64  +  4  inches,  and  hence  the  twist  inserted  must  be  in  accordance  therewith. 

Twist  per  inch  required  in  the  yarn  wound  =  ^^24  x  3-75  =  18-4 

/.  Twist  per  draw  =  68  inches  x  18'4  =  1250 

According  to  par.  (^3),  p.  163,  the  gear  should  be — tracing  the  train  from  the  rim 
shaft  to  the  F.R. :  17  driving  45,  27  driving  35,  17  driving  38  =  1250  revolutions 
of  rim  per  draw;  and  therefore  ^p  =  18*4  twist  per  inch,  this  being  with  a 
12-inch  rim  pulley  and  at  the  rate  of  7520  revolutions  of  the  spindle  per  minute. 

The  Size  of  Eim. — The  rate  of  the  spindle  required  is  9500  revolutions  per 
minute,  actual;  hence,  with  the  rim  shaft  making  940  revolutions  per  minute, 
and  the  size  of  the  rim  x,  and  10  per  cent,  allowed  for  slippage,  the  following 
equation  is  obtained  : — 

940  X  a;  X  6      9500  x  100      .^... 
=  10555 


12  X  I       ~  90 

10555  X  12  X  I      i^o,         .„  .    , 

.'.  X  = pT-fT. 75 — ~  =  16*85,  say  17  inches 

940  X  6  '     -^ 

The  revolutions  of  the  spindles  per  draw,  actual  =  1250 

Allowing  for  slippage,  the  calculated  revolutions  of  spindle  per  draw  =  1390 

Proof  that  the  above  is  satisfactory : — 

The  Speed  Train  of  Wheels. — The  train  connecting  the  rollers  with  the  spindles 

1390 
must  therefore  have  a  value  of  ^tt-^  =  68-3. 

This  means  that  the  spindle  must  be  calculated  to  move  68*3  revolutions 
per  1  of  the  F.E.,  and  hence  the  following  equation,  when  the  speed  wheel  has 
the  value  x : — 

68-3  X  f  X  12  X  17  X  27  X  17  _  .      _  „. 

6  X  17  X  a;   X  35  X  38  ~  . .  x  -  60  i 

Alternative  sizes  of  suitable  wheels : — 

The  smallest  speed  wheel  practicable  being  40  (40-60),  and  the  ratio  required 

17 
between  this  and  the  wheel  on  the  speed  shaft  being  ^^,  the  follo'W'ing  other 

wheels,  within  the  range  of  accommodation,  will  give,  approximately,  the  desired 

,       23    24   25   26   wheel  on  rim  shaft 
results:  ^g,  ^,  -^,  g-^,        gpeed  wheel       " 

The  draft  required  in  the  rollers  is  that  necessary  to  attenuate  3'  roving 


174  COTTON   SPINNING  CALCULATIONS 

into  24'  =  --g^  =  8.      B}-  assuming    x   tlie   draft  claange  pinion,   the  following 
equation  is  obtained  :  — 

54  X  130  X  1      Q  .  54  X  130      ^.  -^.  .,  _.  ,  ^ 

-^ .  =8  :.x-  ^ -^  =  55,  Draft  pinion 

a;xl6xl  8x16 

12  X  a/24      12  X  24 

Builder  Avlieel  =    ^  y    +     .      t    =  10-4  +  18  =  say  28 

2 »/ 8  /  X  o 

Exercise  7. — The  draft  for  28'  W,  from  3'  single  roving  =  ^^  =  9J. 
Assuming  x  the  draft  change  pinion,  and  54  the  B.E.W.,  the  following  equation 
is  obtained : — 

54  X  130  X  1      oi  .  54      3  X  130       .^  t^    ..    •  • 

.   X   16   X  1  =^^  •  •  ^  =  28  >^  -16--  =  ^^'  ^''^'  P^"^°^ 

The  size  of  rim  necessary  to  obtain  the  rate  of  rotation  of  the  spindles, 
10,500  +  10  per  cent,  for  loss,  may  be  obtained  from  the  following  equation,  when 
X  =  the  size  of  the  rim  in  inches  : — 

„.,       X       6       10500x100      ...Q^ 
940  X  Y^  X  ^  =  OQ =  11680 

940  X  6  1 


11680  X  12  X  f  ~  a; 


11680  X   12  X  ?-        X        io  ^K  in  •      1  T>-   , 

.".  TTTK T. — ~  =  T  =  18-65,  say  19  inches,  Eim 

940  X  6  1  '     •' 

The  twist  per  inch  =  ^Wx  3-25  =  17-2 
Therefore  the  twist  per  draw  (68  inches)  =  17*2  x  68  inches  =  1170 
Assuming  the  front  roller  makes  20y*j-  revolutions  per  draw,  and  the  speed 
wheel  contains  x  teeth,  the  following  equation  contains  the  value  of  x,  allowing 
10  per  cent,  for  slippage  : — 

4       38  X  35  X  x  X  19  X  6  _  1170  x  100  _ 
^^11  ^  20  X  35  X  30  X  12  x  §  ~         90 

1300  X  20  X  35  X  30  X  12  X  f      x      „nr,  ^       i     i.    i 

•*•    — oTs^i q5 OK iQ ?^  =  T  =  79*7,  Speed  wheel 

20y\  X  38  X  35  X  19  X  6  1  ^ 

This  wheel  being  too  large,  a  pair  of  wheels  of  suitable  size  may  be  obtained 
from  the  ratio  provided  by  these  change  wheels,  therefore — 

driver         30  20 

or  7077'  say  xq 


driven'  "   79-7'     ''  53 

The  gain  wheels  necessary  to  give  3  inches  "  gain  "  are — 

75  64  —  3 

3-  X  TTp;  X  X  =  — —, —  revolutions  of  the  front  roller  =  19  4 
"^      bO  ^ 

here  x  =  the  value  of  the  ^-^ ,  change  wheels 

driver 

•  ^-^      75  ,Q,  .  60  X  19-4       .  „, 

•  •  3|  X  ^,.  X  a;  =  19-4  .•.  x  =  ^-^ ^r^  =  4-31 

60  3*6  X  75 


AND  COSTS   OF   YARN  175 

Any  pair  of  wlieels  witliin  the  range  of  size  applicable  and  having  this  ratio 
would  suffice. 

.-.  4:31  =  say  26 
These  would  give  the  nearest  to  that  required. 

The  builder  wheel  =  ^^  ^  ^^^  +  ^^-^^  x    ^'  ""  ^"    =  208,  say  21. 

Note. — The  differences  in  the  size  of  the  cop  required  \vill  affect  the  wheel 
directly  proportional  to  their  areas,  and  therefore  as  their  diameters^  (squared). 

Exercise  13. — The  draft  required  to  attenuate  the  13-hank  roving,  double, 
to  80-  =  ^^^  =  12-3. 

The  ratio  of  the  draft  change  wheels,  x,  is  found  as  follows : — 

10  Q      130  .   12-3  X  IG  .  ... 

12-3  =  j^xx  .-.  — ^3Q-  =  X  =  1-5U 

„  ,.        driven       B.R.W.      59        56        53 

Katio  =  -J-. —  or  — r-^ —  =  ^^,  or  ^^,  or  ^7^ 

driver        pinion       39'      37'       35 

The  revolutions  of  the  rim  shaft  per  draw — 

Twist  per  inch  =  3*6^80  =  32*2 
„        draw  =  32-2  x  68  =  2189 

The  size  of  rim,  a;,  allowing  for  10  per  cent,  for  slippage — 

-.„       X  ^6      9000  x  100  10000  x  12  x  |      ^,^„ 

=  ^^0Xj2X|=— yo—  -^--750    X   6  -^Q 

The  speed  change  wheels  ratio,  x,  assuming  no  pause  twisting  at  the  head, 
and  the  gain  4  inches  ;  is  found  as  follows  : — 

2189x100^1x12  27x17      60-4      .„  ^  , , ,  „  , 

X  I ^  XXX  o^- — 5^  =  — i7^r—  =  17-8  revs,  of  h  .R,  per  draw 


90     6  X  20      35  X  38    ^f 

_   17-8  X  90  X  6  X  20  X  35  X  38 
*  ~  2189  X  100  X  0-75  x  12  x  27  x  17 


=  0-283 


Therefore  the  only  possible  wheels  within  the  ranges  specified  in  Fig.  33 

60 
arej^. 

Gain. — The  revolutions  of  the  back  shaft  and  front  roller  required  per  draw 
respectively,  being  3*38  and  17-8,  the  following  equation  gives  the  value  of  x, 
the  gain  change  wheel  ratio  : — 

9QQ       75  ,-_  .  17-8x60       .„, 

3-38  X  g-^  X  a:  =  17-8  •*•«=  =  3-38  x  75  =  ^^1 


176  COTTON   SPINNING  CALCULATIONS 

The  pair  of  wheels  within  the  range  specified  having  the  nearest  to  this 

105  gain 

ratio  are  tf-,  — -. — ^^ r — 1« 

15    gain  boss  wheel 

The  builder  wheel  =  1^^  +  "^-^  x  ^^^  57 
2V8  2x8  my 

100  X  2 
Exercise  16. — The  draft  required  in  the  rollers  =  — ^n —  =  ^^• 

The  draft  change  wheels  ratio,  x,  must  be — 


-V^,"-  X  :c  =  10 

_  10  X  16  _  160 
•'•  ^  ~      130  130 


=  V2[ 


Therefore  the  suitable  draft  wheels  are — 

B.B.W.  ^  48   53   54 
P.W.    ~  39'  43'  44 

The  twist  per  inch  required  =  3*18^100 

draw       „        =  64  X  3-18^100  =  2035 

Allowing  for  10  per  cent,  loss,  the  calculated  revolutions  of  the  spindles  per 

.     .      2035  X  10      ,„oo 
draw  required  = „ =  ^zdS. 

The  actual  revolutions  per  minute  of  the  spindles  required  =  8000 

^      ,                                                                          8000  X  10 
.*.    „  calculated  „  „  „       — g 

With  the  size  of  rim  required  570  x  ;r7,  x  -g 


X  10  X  I      in.r 

••"=        570x6    "  =  19-5  say 

The  revolutions  of  the  front  roller  per  draw  required  =  — -^ —  =  17*8 

^   r  ca       ■        X.  a  1  ^888  X  10  X  |        ,,„ 

The  revolutions  of  the  rim  shaft  per  draw  = -^^ — -^— ^  =  143 

The  speed  change  wheels  ratio,  x,  is  therefore — 

17-8  X  ^"^  X  3^  X  a;  -  143        x-  ^-^^  ^-il^^^  -  1-755 
17  8  X  ^-^  X  g^  X  a;  -  14d        x-  ^^.^  x  60  x  35  "  ^  '^^ 

Therefore  any  of  the  following  pairs  of  wheels  would  be  suitable  : — 

speed  wheel    _  42    44   49    51 
rimlhaft  wheel  ~  24'  25'  28'  29 


AND   COSTS   OF  YARN 


177 


Gain.— The  revolutions  of  the  back  sliaft  and  front  roller  reiiuired  per  draw, 
respectively,  being  3-38  and  17-8,  the  following  equation  gives  the  value  of  x 
the  gain  change  wheels  ratio  : — 


3-38  X  /.iJ  X  cc  =  17-8 


X  =  4-21 


And  hence  the  following  pair  of  these  wheels  are  most  suitable — 
105  _      gain  wheel 


15       gain  boss  wheel 

+ 


rr,     1    -n        11       12V100   ,   12x100 
The  builder  wheel  — 


2V8 


X   ^'^^"l   -  47 

2x8         (\if  ~ 


Particulars  of  Gearing  in  *'  Dobson's  Ord."  Mule.— Fig.  34  shows 


Fig.  34. 

the  arrangement   of  the   gearing  in   mules   for    medium    and 
medium  fine  counts  as  made  by  Dobson  and  Barlow. 

The  following  are  particulars  of  the  various  trains  and  the 
range  in  the  size  of  the  wheels  shown  :  — 

N 


178  COTTON   SPINNING   CALCULATIONS 

(rt)  Train  to  Sjnndles. — Revolutions  of  the  rim  shaft  (H  G) 
per  minute  from  400  to  850  per  minute.  Eim  pulley,  D,  12- 
22  inches ;  tin  roller  pulley,  D3,  10-12  inches  ;  tin  roller,  U, 
6  inches ;  spindle  wharves,  vi,  3-4  inches. 

(h)  Train  to  the  Rollers.— J,  19 ;  K,  58 ;  L,  30-56  ;  C,  60- 
100  ;  R,  32 ;  S,  25. 

(c)  Roller  draft  gear  :  7c,  20  ;  Z,  180  ;  A,  30-60 ;  m,  30-70. 

Diameters  of  rollers  :  front,  1  inch ;  middle,  |  inch ;  back, 
1  inch, 

{(1)  Train  to  the  Bach  Shaft  from  the  Front  Boiler  Shaft. — T, 
51-55;  0,  55;  E,  70-78;  P,  16-20;  Q,  68;  M,  15:  N,  55. 

Revolutions  of  the  back  shaft  per  draw  :  3*5  for  64-inch 
draw  ;    3*28  for  60-inch  draw  ;  3*06  for  56-inch  draw. 

(e)  Train  for  Slow  Boiler  Turning,  sometimes  called  the 
Eeceding  Motion.— JJ,  20;  V,  40;  W,  1 ;  X,  30;  Y,  24;  Z,  24. 

Train  for  Holler  Delivery  during  the  Inward  Run. — i, 
14-17  ;i,  40. 

Taking-in  and  Baching-off  Motion  Gear. — a,  14  inches  ;  c,  17  ; 
/,  24 ;  (7,  14  ;  h,  40 ;  c,  10 ;  d,  73. 

Taking-in  motion  shaft,  a  :   170-350  per  minute. 

Revolutions  of  taking-in  motion  shaft  (/  per  64-inch  draw,  3. 

Building  or  Shaper  Motion. — Wheel,  12-70,  and  various 
pitch  of  screws. 

Twist  Wheel— ^0-120. 

ExEKciSES. — Ascertain  the  following,  from  the  particulars  contained  in 
Fig.  34  :— 

1.  The  range  in  the  rates  per  minute  at  which  the  spinrlles  may  be  driven. 

2.  The  range  in  the  twist  that  may  be  inserted  in  the  yarn. 

3.  The  range  in  the  draft. 

4.  The  range  in  the  counts,  twist  and  weft,  which  the  machine  is  adapted  for 
in  the  respect  of  twisting  with  the  normal  twist  constants. 

5.  The  ratio  in  the  movement  of  the  carriage  before  and  under  the  influence 
of  the  jacking  motion,  assuming  that  during  the  former  movement  the  drawing- 
out  band  is  on  the  full-sized  portion  of  the  scroll ;  and  at  the  termination  of  the 
latter  movement,  on  the  half-sized  portion  of  that  part. 

6.  The  ratio  of  the  roller  and  carriage  movements  during  twisting  at  the 
head  and  when  in  ordinary  action. 

7.  The  ratio  in  the  rates  of  the  spindles  during  spinning  and  Avhen  backing-off. 

8.  The  time,  in  seconds,  taken  to  move  the  carriage-in,  at  the  slowest  and 
quickest  rates. 

9.  The  length,  in  inches,  delivered  by  the  rollers  during  the  inward  run. 


AND   COSTS   OF   YAEN  179 

Answers — 

1.  3200-14,960. 

2.  7'28-44-5. 

3.  4-5-21. 

4.  4-0^  twist,  5''-25  weft  to  210'  weft,  152"  twist. 

In  the  above  calculation,  the  calculated  twist  is  as  obtained  without  the  use 
of  twist  wheels.  By  using  twist  wheels,  the  twist  may  be  extended  to  suffice  for 
all  practical  rctiuirements,  taking  the  above  as  representing  f  of  the  possible 
twist  then  the  range  could  be  extended  to  78'4  turns  per  inch. 

Example  in  respect  of  Exercise  5. — The  difference  in  the  train  pulling  out 
the  carnage  during  jacking :  R,  S,  being  in  abeyance,  and  the  motion  is  obtained 
through  M.  N. 

The  train  prior  to  jacking,  from  the  side  shaft,  is  E,  S,  T,  0,  E,  P,  Q  ;  and 
during  jacking  M,  N,  0,  E,  P,  Q. 

mu    A-cv  •    .,  1  32    55    16       ,  15   55    16         32       , 

The  difference  m  these  values  are  '  i^i  n7\<  fs  ^^^^^  rE>  ^-n^  po>  or,  ^  >  and 

15 

^  respectively,  or  3'5  :  1. 

This  is  the  ratio,  when  jacking  is  proceeding,  with  the  drawing-out  band 
wound  upon  the  full-sized  portion  of  the  scroll.  As  the  scroll  portion  is  gradu- 
ally brought  into  action  this  ratio  increases.  When  the  half-size  portion  is  acting, 
the  reduction  in  the  rate  of  the  movement  has  attained  3*5  x  2  =  1,  of  the 
normal  rate. 

Exam2)le  in  respect  of  Exercise  6. — The  difference  in  the  trains  driving  the 
rollers  whilst  the  carriage  is  at  rest,  and  twisting  "  at  the  head,"  is  as  follows  : — 

The  wheel  train  RS  is  in  abeyance,  and  motion  is  obtained  through  train 

U,  V,  W,  X,  Y,  Z,  and  therefore— 

32         20      1     24 
The  values  of  these  trains  are  respectively  .^Z  and  jr.,    ^,  ^,  or  as  77  :  1. 

Example  in  respect  of  Exercise  7. — The  difference  in  driving  the  spindles 
during  spinning  and  "  backing-off  "  are  respectively — 

Lowest  rate  of  the  rim  shaft  during  spinning,  400 

.„  170  X  10 


"  backing-off,' 


73 


and  therefore  the  rate  of  the  spindle  during  the  latter  period  is  z.rf7-. ^j^  times 

less  than  during  the  former  period  =  slightly  more  than  ■^. 

Example  in  respect  of  Exercise  8. — Assuming  the  taking-in  scroll  shaft  makes 
3  revolutions  per  draw  of  62  inches,  the  time  in  seconds  taken  to  draw  the 
carriage  in,  is — 

3 

lowest  rate  .-„^ ,^^ ^  x  60  =  4'27  seconds 

170  X  \'i   xji 

or,  average  rate,  14^  inches  per  second. 


180  COTTON  SPINNING  CALCULATIONS 

Example  in  respect  of  Exercise  9. — Assuming  the  back  shaft  makes  3*39 
revolutions  during  the  drawing  in  of  the  carriage  and  the  17  wheel  is  in  use  on 
the  back  shaft,  the  length  delivered,  equals — 

17      1"  X  22 
3-39  X  -77.  X = —  =  4-52  inches 

Exercises. — Ascertain  the  production  in  hanks  per  55  hours,  without 
allowances  for  stoppages ;  and  the  various  change  wheels  necessary  to  adapt  the 
gearing,  as  contained  in  Fig.  34,  for  the  undermentioned  counts  and  conditions 
of  production. 

Allowances :  For  slippage,  in  driving  the  spindles  from  the  rim  shaft,  10  per 
cent. ;  draw,  60  +  4^  inches,  the  latter  delivered  during  the  inward  run  ;  backing- 
ofif  and  run-in  to  occupy  5  seconds ;  loss  of  speed  due  to  changes,  10  per  cent. 

1.  GO  W.  from  10-hank  double  roving,  Egvptian :  actual  speeds  of  rim  and 
spindles,  850  and  10,000  revolutions  per  minute ;  gain,  1  inch ;  jacking,  1  inch  ; 
5  per  cent,  of  twist  being  inserted  after  jacking. 

2.  60  T.  from  12-hank  double  roving,  Egyptian :  rim  and  spindle  speeds,  840 
and  10,000  revolutions  per  minute  actual ;  gain,  U  inch ;  jacking,  1  inch ;  12  per 
cent,  of  twisting  after  jacking. 

3.  80  W.  from  14-hank  double  roving,  Egyptian :  rim  and  -spindle  speeds, 
840  and  9000  revolutions  per  minute  actual ;  gain,  2  inches ;  jacking,  1 }  inch ; 
8  per  cent,  of  twisting  after  jacking. 

4.  80  T.  from  16-hank  double  roving,  Egyptian :  rim  and  spindle  speeds, 
840  and  9500  revolutions  per  minute  actual ;  gain,  2  inches ;  jacking,  2  inclies ; 
12|  per  cent,  of  twisting  after  jacking. 

5.  94  W.  from  16-hank  double  roving,  Egyptian :  rim  and  spindle  speeds, 
840  and  8700  revolutions  per  minute  actual ;  gain,  2  inches ;  jacking,  2  inches  ; 
10  per  cent,  of  twisting  after  jacking. 

6.  90  T.  from  16-hank  double  roving,  Egyptian:  rim  and  spindle  speeds, 
840  and  8700  revolutions  per  minute  actual ;  gain,  1  inch ;  jacking,  2^  inches ; 
12^  per  cent,  of  twistmg  after  jacking. 

Example  of  working  Exercise  1. — The  spindle  speed  will  be  attained   by 
using  a  rim  and  tin  roller  pulleys  of  the  following  diameter : — 
Let  X  =  the  spindle  speed  change  ratio  ; 

then  860  X  .  X  «  =  ^-^^  .:  .  =  ^m  =  1-634 

.'.  18  inches  R.P.  and  11  inches  T.E.P.  or,  others  giving  this  ratio. 

The  revolutions  of  the  rim  shaft  per  draw  must  be — 

GO  -h  4i  X  3-18 /6U  _  .    , 

18   "6 Tiu ^^^ 

II  ^  V  ^  100 


AND   COSTS   OF   YARN  181 

The  speed  change  gear  must  be  arranged  to  obtain  the  delivery  of  60  -  2  inches 

3*28  X  59 
whilst  the  back  shaft  is  moving  the  carriage  out  59  inches,  and  therefore  the  — -gQ — 

revolutions  of  the  back  shaft  are  required  in  the  same  period.  During  this  move- 
ment the  spindles  are  required  to  insert  twist  in  accordance  with  the  state 
specified,  i.e.  100  per  cent.  —  5  per  cent.  —  x  per  cent,  twisting  during  jacking. 
During  "jacking  "  the  carriage  is  assumed  to  move  at  f  the  normal  rate,  and  there- 
fore requires  a  period  equal  to  that  required  to  move  the  carriage  3^  inches  at  the 
latter  rate.  Hence,  95  per  cent,  of  the  twisting  equals  the  period  required  for 
59  +  31  inches  of  movement  at  the  normal  rate,  and  therefore  the  revolutions  of 
the  rim,  during  the  above  59  inches,  must  be — 

roi        =  8^1  P^^  cent,  of  135  =  120  revolutions  of  rim 

During  the  run  out  of  the  carriage,  the  front  roller  is  required  to  deliver 
58  inches,  and  therefore  it  must  make — 

58 


1  X  -T-- 


=  18'43  revolutions 


The  speed  change  gear  ratio  {x)  is  therefore — 

120  X  \%  XXX  ^  =  18-43     .-.    X  =  ^fon-^f  \^^  =  0-366 
^*'  -■>  120  X  19  X  d2 

The  speed  change  wheels,  within  the  range  having  this  value,  are — 

driver  34    _35     36      37      38      39     40 
driven  lOr  104'  107'  110'  113'  116'  119 

3-28  X  59 
TJie  "gain"  change  gear  must  be  arranged  to  impart         „^ —  revolutions 

to   the  back  shaft  per   18-43  revolutions  of  the   front  roller,  before  jacking 
commences.     Therefore  the  gain  change  wheel  ratio  (x)  must  be — 

,„  ,„      55  3-28x59  3-28x59x68       ..... 

18-43  X  .T5  x  a;  = ^,7:^ /.  x  =  -^~r^ ^^ — ^  -  0-216 

68  60  12-43  X  60  X  55 

The  change  wheels  nearest  to  this  value  are — 

driver  16  ^ 

driven  74 

TJie  draft  and  draft  change  wheels, — A  10-hank  double  rove  would  necessitate 

a  draft  of  -^^  =  12,  if  the  draft  due  to  gain  and  jacking  is  neglected. 

Taking  the  latter  into  account,  it  would  l)e — 

12x621      ^.. 


182  COTTON   SPINNING  CALCULATIONS 

The  draft  change  wheel  ratio  (x)  to  give  tlie  latter  draft  must  be — 

-L8^  xx=  11-6  .-.  X  =  ^-^^^^  =  1-29 

The  draft  change  wheels,  within  the  range  specified,  containing  this  value- 
driven  _  62     58     53     49 
driver  "  48'    45'    41'    38 

Twist  wlieeJs  are  necessary  when  the  rim  shaft  is  required  to  rotate  a 
definite  amount  after  the  carriage  has  reached  the  "  head."  Usually  it  is 
most  convenient  to  arrange  them  to  make  one  or  two  revolutions  per  draw, 
and  therefore,  in  this  instance,  since  135  is  not  available,  ip,  say  G8. 

rr-  1  135      60  X  100       ^       ,^,,     ,     ,,,, 

Time  per  draw  =  gjQ  x  — ^-^ —  +  5  =  10-15+5  =  15-15  sees. 

TT    1  •  ;ii  1       60  X  60  X  55  X  64^      „„  „ 

Hanks  per  spmdle  per  week  =  — tttk o^ ottt^  =  27*8 

il5-15  X  36  X  840 

Examj)Ie  of  working  Exercise  6. — The  required  speed  of  spindle  will  be 
obtained  when  the  change  pulleys  in  the  gear  from  the  rim  to  the  spindles  have 
the  ratio  x  in  the  following  equation  : — 

.*.  a  =  1-44 
.'.  ratio  =  rp  p  p  =  11  nearest 
Tlierefore  the  revolutions  of  the  rim  per  draw,  if  the  latter  are  adopted— 
-  CO  +  4^  X  3-6  X  V90  X  100  _  ^.„ 

16    w~:       — "^^^ 

zy  X  ij  X  90 

Note. — The  ^^  is  the  slippage. 

The  speed  change  gear  must  be  arranged  to  obtain  the  delivery  of  60  —  3^  inches 

whilst  the  carriage  moves  57-^  inches  outward,  and  therefore  the  back  shaft  makes 

3-28  X  57V'  '. 

pjTT — ^  =  3-14  reA'olutions   during   this   roller   movement.     The   spindles 

are  required  to   insert  twist  amounting  to  the  following,  in  the  same  period, 

210  X  87i  X  57- 

and  hence zrj~ ~  revolutions  of  rim  per  draw  =  159. 

100  X  6b|  ^ 

573  . 

^pf  is  the  fraction  of  87J  per  cent,  of  210  revolutions,  during  which  time  the 

carriage  and  rollers  are  moving  at  the  normal  rate.     This  is  ascertained  from  the 
rate  of  jacking  proceeding  at  ^  slower  than  the  normal  rate,  the  jacking  rate 

being  from  05;  to  i  the  normal  depending  upon  the  extent  of  the  scrolled  portion 
of  the  drawing-out  barrels,  on  the  back  shaft,  in  action, 


AND   COSTS   OF   YARN  183 

The  front  roller  is  therefore  required  to  make  ~, — -  -  revolutions  prior  to 

1  X  --f-  ^ 

jacking,  and  whilst  the  rim  shaft  makes  159  revolutions,  and  hence  the  speed 
change  wheels  ratio,  x,  is  contained  in  the  following  equation  :— 

159  X  >^  X  a;  X  „^  =  - — i.,  =  18 
58  2o      1  X  --J^ 

.       _  18   X  58  X  25  _     . 

"  ^      159  X  19  X  32  "    '" 

The  speed  change  wheels  nearest  to  this  value  are  ,??r  '^^^. 

111  driven 

The  111  wheel  is  beyond  the  range  stated  on  the  figure,  but  in  this  case  110 
would  probably  suffice ;  if  not,  it  would  then  be  necessary  to  make  an  alteration 
in  some  other  wheel  of  this  train.  For  values  lower  than  0-27,  the  most  con- 
venient alteration  is  R. 

The  "  Gain  "  Chainje  Wheels  must  be  arranged  to  give  3-14  revolutions  to  the 
back  shaft  whilst  the  rollers  make  18 ;  therefore  the  gain  change  wheels  ratio, 
X,  must  be — 

18  X  tg  X  cc  =  3-14  /.  X  =  ^^^  =  0-216 

The  "  gain  "  change  wheels  having  this  ratio  and  within  the  ranges  specified 

10 
are:^^. 

The  Draft  and  Draft  Change  Wheels.— A  IG-hank  double  rove  will  necessi- 

90 
a  draft  of  ^^  =  11],  if  allowance 

Allowing  for  the  latter,  it  would  be — 


90 
tate  a  draft  of  ^  =  11],  if  allowance  is  not  made  for  "gaining"  and  jacking 


Hi  X  g^^j  =  10-G^ 


*2 


The  draft  change  wheel  ratio,  x,  is  contained  in  the  equation — 
^A  xx  =  10-63        .-.  X  =  1-18 

Therefore  the  draft  change  wheels  suitable  are — 

driven  _  53    59    65    66 
driver  ~  45'  50'  55'  56 

The  time  per  draw  in  seconds  =  |!^  ^  ?  ^  l^i^  +  5  =  21-7 

840  X   1    X   90 

The  hanks  per  spindle  per  week  =  ^A^^^'^P^  =  19-5 

21-7     X  36  X  840 

Mule  Calculations. — Figs.  36  and  37  show  the  gearing  as  in  Piatt's  mules. 
The  following  examples  are  taken  from  those  figures. 

Motor  drum,  800  revolutions  and  11  inches  diameter.  Line  shaft  drum  driven 
from  the  motor,  38  inches  diameter ;  for  driving  the  mule,  28  inches.  Counter 
shaft  drums  :  driven,  18  ;  driver,  24  ;  grooved  pulley  for  T-up  motion,  12  inches. 


184  COTTON   SPINNING  CALCULATIONS 

The  revolutions  of  back  shaft  for  G2i-inch  draw  =  3i 
„  „  „  60  „  =  3-65 

„  „  „  58^       „  =  3-56 

Alterations  for  counts  100'  from  double  18  hank  Sea  Islands  JRove,  assuming 
the  present  speed  of  spindle  suitable. 
The  present  speed  of  spindle 

o^„      11  X  28  X  24  X  16  X  6      p.-,Q„  _         ,  ,.  .     , 

=  800  X  jTTs Tn tt; T^ Q  =  6287 "7  revolutions  per  mmute 

38  X  18  X  16  X  11  X  f  ^ 

Twist  constant  =  3-6 
,,     per  inch  =  36 
Twist  per  draw  of  62"  put  up,  i.e.  58V'  +  3i"  =  62"  x  ^m  x  3-6  =  2232 

The  revolutions  of  the  rim  must  be  such  as  will  give  2232  revolutions  of  spindle 
per  draw. 

Assuming  a  loss  of  5  per  cent,  in  transmitting  the  motion  to  the  spindle 
from  the  rim  shaft,  then  the  revolutions  of  the  rim  shaft  per  draw  should 
be— 

2232  X  100  X  11  X  0-75  ^.^ 

TT^ — . ^^  =  say  202 

95   X  10  X    b  '' 

The  duty  of  the  twist  wheel  is  to  control  the  revolutions  per  draw  of  the  rim 
shaft.  In  this  case  the  twist  wheel  divided  by  2  equals  the  revolutions  of  the  rim 
shaft. 

.-.  2A2  =  twist  wheel  =  101 

If  there  were  no  gain  between  the  movement  of  the  caftiage  as  compared 
with  the  length  delivered  by  the  front  roller,  then  the  rollers  must  deliver,  during 
the  outward  run  of  the  carriage,  58^  inches,  and  therefore  the  front  roller  must 
make — 

^„     ^,,  =  17-518  revolutions,  say  17-52 


The  present  gear  would  deliver — 

202  X  ,^ 7^ oTs  =  30-3  revolutions  of  front  roller  instead  of  17-52 

70  X  60  X  30 

Therefore  if  the  change  be  made  at  the  speed  wheel,  a  — TnTKr, —  =  10^   wheel 

would  be  necessary. 

Such  a  large  wheel  would  probably  be  impracticable.  Usually  the  driver  of 
the  speed  wheel  is  constituted  a  change  wheel,  in  which  case  the  extent  of  the 
dilTerence  in  the  change  practicable,  in  the  speed  wheel,  and  that  required,  would 
be  possible  at  the  driver  Avheel. 

Assuming  that  up  to  90  are  the  available  sizes  of  speed  wheels,  then  the 
speed  wheel  driver  would  need  to  contain— 

^-^  =  62  teeth 

104 


AND   COSTS   OF   YAEN  185 

N.B, — III  such  a  case  it  would  be  unnecessary  to  use  the  twist  wheel,  as  the 
fact  of  the  carriage  getting  out  to  the  head  would  control  the  revolutions  of  the 
rim,  but  less  accurately. 

No  Gain. — The  gain  wheel  and  its  train  controls  the  ratio  in  the  movement 
of  the  carriage  relative  to  the  spindle.  The  rollers  must  necessarily  deliver  58} 
inches,  and  the  carriage  must  move  that  amount. 

The  movement  of  the  back  shaft  in  drawing  the  carriage  out  G2?,-inch  draw 
is  given  at  3*   revolutions.     Therefore,  for  58^-inch,  proportional  movement 

34  ^  531 
\vill  be  required,  or  —  t.^, — -  =  3-56,  instead  of  3-8. 

0<iTy 

Should  this  be  the  case,  then  the  front  roller  must  make  ^^ — ^— ;  revolu- 

IB    -^      7 

tions,  whilst  the  back  shaft  makes  3-56  revolutions  ;  therefore  the  revolutions  of 
the  front  roller  =  17-52. 

Note.— Variations  in  the  tension  and  size  of  drawing-out  bands  will  cause 
variations  in  the  revolutions  of  the  back  shaft  per  draw. 

With  the  present  gear  the  revolutions  of  the  front  roller  per  3*56  revolutions 
of  the  back  shaft,  are  (see  p.  192) — 


3-5G  = 


/revolutions  of  F.R.  x  20\      /revolutions  of  F.R.  x  40^ 
V  2  X  60  j  "^  I  2  X  40  y 


(revolutions  of  F.R.  .  revolutions  of  F.R.\  „/.       .k 
__ + 3G  X  45 
..  ^u^  - ^ 2 / 

60  X  90 

/revolutions  of  F.R.      3  revolutions  of  F.R.\  G 
•■•  3-^«  =  \ 6 + 6 J20 

•    a  KR  _  '^^       6  _  4a3  _  a; 

..d-ob_-g  X2-Q-20-5 

.-.  3-56  X  5  =  a; 

.-.  X  =  17-80  revolutions  of  F.R. 

The  gain  wheel  must  therefore  be  altered  to  give   17*52  revolutions,  and 
therefore — 


3-56  = 


/17-52  X  2^\   /17-52  x  40\ 
V  2  x  60  /   V  2  X  40  } 


60   G.W. 
36  ^  45 


/17-52  ,  17-52\_   ,, 
(^-g-  +  -2-J36x45 


3-56   

60  X  G.W. 


186 


COTTON  SPINNING  CALCULATIONS 


/17;52 


Sx  17-52^ 

6     \ 


36  X  45 


GU  X  (i.W 


.  „  _  70-08      3G        45 
..6-bb-     ^      Xg-^x^^^,-^ 


1 


3-56  X   6   X  GO 

70-08  X  3G  X  45  ~  G.W. 

70-08  X  3G  X  45     G.W. 


3-56   X   G   X  GO 


1 


70-08  X  9 
^56^>r2 


.-.  G.W.  =    :^v~-  =  88-5,  say  80  or  88 

"  "  Gain  "  CImnges. — The  36  gain  boss  wheel  combined  with  an  88*5,  gives, 
according  to  previous  calculations,  a  delivery  by  front  roller  of  58-5  inches, 
Taking  this  as  a  basis,  the  amount,  in  inches,  delivered  by  the  front  roller  per 
3-56  revolutions  of  the  back  shaft,  with  various  other  sizes  of  gain  wheels,  is  as 
follows  : — 


Gain  boss 
wheel. 


36 

36 

36 

36 

36 

36 

36 

36 

36 

35 

34 

37 
36 


Gain  wheel. 


88 

87 

86 

85 

89 

90 

91 

92 

90 

90 

90 

90 
91 


58J  X 

88-5 

88 
58-5  X 

88-5 

87 
58-5  X 

88-5 

86 
58-5  X 

88  5 

85 
58-5  X 

88-5 

89 
58-5  X 

88-5 

90 
58-5  X 

88-5 

91 
58-5  X 

88-5 

92 
58-5  X 

88-5 

90 
57-52  X  36 

85 
57*52  X  36 

34 
.57-52  X  36 

37 

56-89 

58  83 

59-5 

60-2 

60-9 

58-17 

57-52 

56-89 

56-26 

57-52 

59-16 

G09 

55-9 


Variations  in  count 
resulting. 


99-5 

98-4 

97-2 

96-0 

100-5 

101-6 

102-S 

1040 

101-G 

99-0 

960 

104-6 
102-8 


AND   COSTS   OF  YARN 


187 


Gain  boss 
wheel. 

Gain  wheel. 

Variations  in  count 
resulting. 

35 

91 

"'=■«!.>'''=      58  31 

100-5 

34 

91 

''■'I''  ""  =  6002 

97-2 

37 

01 

56-89  X  36       „  „. 
_  oo-3o 

10.-.  8 

36 

89 

5817  -  0-2S  ("gain) 

100-6 

35 

89 

59-83  +  1-33      „ 

97-8 

34 

89 

61-32  +  2-82      „ 

95-4 

37 

89 

56-6  -  1-9 

103-3 

36 

88 

58-83  +  0-33      „ 

99-4 

35 

88 

00-51  +  1-01      „ 

90-7 

37 

88 

57-24  -  1-26       „ 

102-0 

The  effect  of  gain  on  the  counts  of  the  yarn  spun  (see  right-hand  cohimn). 

The  EoUer  Draft  Wheel. — The  draft  necessary  to  attenuate  two  ends  of  18' 
rove,  so  that  it  is  delivered  by  the  F.R.  100'  count,  must  be — 

l-^'-lUorXon 
jLa    ~"      '•"        'J 

The  ratio  in  the  surface  movements  of  the  front  and  back  rollers  respectively, 
must  therefore  be  100  :  9.  With  the  diameters  of  those  two  parts  alike,  and  the 
draft  wheels  as  given,  then  the  pinion  wheel  (x)  would  need  to  be — 

lOOo; 
9 


54^  140 
X        16 


100        54  X  140 


54  X  140  X  9  ,.T  . 

••      100x16      =«'  =  ^2-5 

Hence,  the  wheel  used  must  either  be  42  or  43  ;  the  count  in  these  instances 
would  be  101"1  or  98-8.  If  the  exact  count  was  required,  it  would  be  necessary 
to  employ  a  pair  of  wheels  having  a  ratio  of  7875  :  10,000, 

Draft  Wheels. — Other  pairs  of  wheels,  giving  a  close  approximate  to  ^-p^J*^, 
are — 


B.R.W.  =    80 

75 

70 

GG 

61 

56 

52 

47 

Pinion  =    63 

59 

55 

52 

48 

44 

41 

37 

■Count  =  100-0 

100-1 

100-2 

99-95 

100-0 

100-2 

99  88 

1000 

Exercise  1. — Assuming  the  spindle  speed  6287  revolutions  per  minute  is  too 
slow,  and  that  it  is  required  to  be  7073,  what  changes  would  be  necessary  ? — 
(1)  To  obtain  the  desired  spindle  speed. 
The  readiest  way  is  by  increasing  the  size  of  the  rim — 

16  X  7073       ,Q  .    ,     . 
~  6287 —  ~  lo-mch  rira 


188  COTTON   SPINNING  CALCULATIONS 

(2)  To  obtain  the  riglit  speed  of  the  carriage  and  rollers  relative  to  the 
spindles,  it  will  be  necessary  to  change  the  speed  wheel. 

Speed  Wheel. — If  90  x  52  constitute  the  driven  and  driver,  change  wheels, 
the  speeding  of  the  spindles  means  that  twisting  takes  place  quicker,  and  there- 
fore the  rollers  must  be  made  to  deliver  quicker  in  like  proportion. 

.     90  X  16  _  720      ..  ,     ,     , 

. .    — .r. —  =  -q-  =  oO  speed  wheel 

The  rate  of  the  production  would  be  the  time  taken  to  twist  G2  inches  of 
yarn,  after  allowing  5  per  cent,  for  loss  in  transmission,  with  the  spindle  making 
6287  revolutions  per  minute. 

rp,     ,.       .  -,    ,  1       ,    ,    .,       22x32x100x60      „„  ,,o 

Ihe  time  in  seconds  taken  to  twist  =  ^ -^ ^-= —  =22-418 

95  X  6  X  287 

The  time  in  seconds  taken  to  backing-oif  and  run  in  =    4-5 

Time  per  draw  =  26-918 

The  production  after  changing,  i.e.  revolutions  of  spindles  to  7074  instead 
of  6287— 

rr-       +    •  ,•           22-418  X  16       ,„„^» 
Time  twisting  = ^-^ =  19  927  sees. 

Time  twisting  backing-off  and  run  in  =    4*5 

Total  time  =  24-427 

Production  in  hanks  per  week  of  55  hours,  in  case  of  18-inch  rim — 

60  X  60  X  55  X  62"       ....,,  .   n 

24-427  X  36  X  840    =  ^^'^^  ^^''^"^^  P'^'  ^P"^*^^' 

Production  in  case  of  16-inch  rim :  when  the  rate  of  spindle  in  revolutions 
per  minute  with  18-inch  rim  is — 

800  .  "JlfS?  24  X  18  X  6  ^,„„ 
38  X  18  X  16  X  11  X  I 

and — 

60  X  60  X  55  X  62"   _  ( production  in  hanks  with  16-inch  rim  on 
26-918  X  36~>r840         \     and  spindle  revolving  6287 
=  15-08 

Exercise  2. — A  mule  making  50'  T.  has  the  following  change  wheels  : 
Draft  pinion,  40;  rim,  18  inches;  speed,  80;  builder,  50.  What  changes  in 
these  would  alter  the  counts  to  36'  with — 

(a)  The  speed  of  spindles  unaltered  ? 

(6)  „  „  increased  \  ? 

Answers — 

(a)  (b) 

Draft  pinion 56  56 

Speed 68  58 

Eim —  21 

Builder  1 47  47 

'  Rule  given  on  p.  1G8  is  here  used. 


AND   COSTS   OF   YARN  189 

ExiiRCisE  3. — x\.  imile  containing  1000  spindles  and  spinning  48',  the  draw 
being  62  +  4  inches,  and  1100  draws  are  made  in  forming  a  set  of  cops.  Find 
the  weight  of  the  set  of  cops,  allowing  2|  per  cent,  for  breakages.    A)is.  48  8  lbs. 

Exercise  4. — The  carriage  in  a  mule,  producing  46'  W.,  is  known  to  move 
G  per  cent,  slower  than  the  front  roller,  single  6-hank  rove  being  used.  Find 
the  draft  required  in  the  rollers.  Ans.  8'17. 

Exercise  5. — A  mule  completes  5  draws  of  64  +  4  inches  each  in  68  seconds 
when  spinning  40'  T.  The  time  occupied  in  backing-off  and  winding  is  4|-  seconds. 
Wliat  will  be  the  calculated  and  maximum  actual  rate  of  revolutions  of  the 
spindles,  assuming  the  slippage  and  loss  of  time,  due  to  reversing,  is  known 
to  be  25  per  cent.  ?     Take  the  twist  standard  for  American  cotton. 


Answer, 


TV-  1  68  -  (5  X  4i)      46? 

Time  per  draw  —  ^ ^  =      ■* 

o  0 


=  9"35  seconds 
Twist  and  actual  revolutions  of  spindle  per  draw  =  375,v/40x68  =  1612 
Calculated  revolutions  of  the  spindle  per  draw  =  3*75v'40  x  68  x  ^fP-  =  2150 

Actual  maximum  rate  of  revolutions  of  spindle  "»  _  3-75^40  x  68  x  60 

per  minute  /  9^35  ~  10620 

Calculated  rate  of  revolutions  of  spindle  perj  _  10620  x  100  _  .,070^ 
minute  /  75  ~  lo7-0 

Exercise  6. — What  would  be  the  production  in  hanks  and  pounds,  per  week 
of  55^  hours,  per  spindle,  and  per  mule  of  1200  spindles,  when  the  following 
allowances  are  made:  8  minutes  per  doff;  9^  hours  for  cleaning;  2h  per 
cent,  for  other  stoppages,  the  cops  weighing  at  the  rate  of  10  per  pound  ? 

Eequired :  the  twist  per  inch  minus  time  per  draw,  and  the  production  in 
hanks  and  ounces  per  spindle,  per  55^  hours,  in  a  mule  making  cops  that  weigh 
10  per  pound,  and  working  under  the  following  conditions  :  Nett  time  worked, 
53  hours ;  allow  2h  per  cent,  for  breakages ;  for  doffing,  8  minutes  per  dofif ; 
counts,  120'  W.  from  combed  special  Egyptian  cotton,  (twist  constant,  3-18). 
Spindles  working  at  two  rates  of  speed — first,  5880,  and  second,  9000  revolutions 
per  minute.  Five-eighths  of  the  twist  only  is  put  in  at  first  speed.  The  backing-off 
and  run  in  occupies  5|  secoads,  and  the  length  of  the  draw  is  58i  +  3|  inches. 

Answer — 

Twist  per  inch  =  3-18^120 
Twist  per  draw  =  3-18^120  x  62  =  2160 

,,,.             ,        .             T       2160  X  5  X  60  2160  x  3  x  60  .   ^, 

Imie  per  draw  m  seconds  ^  ^^^^^^^ sees,  -f-  ^^^^^  ^  ^^   ^  +  5h 

=  13-8  +  5-4  +  bh  =  24-7 

1    ^  120  X  840  X  36 

10      ^        62        — 


190 


COTTOX   SPIXXIXG   CALCULATIONS 


Time  per  doff,  including  dufBng,  \  _  1       120  x  840  x  36      24-7 

/ "  ro  ^  62  ~ 


m  minutes 


60  X  60  "^  60  ^""^' 


=  40-2  +  0-133 


53  X   60   X 


Doff  per  week  = 


971 
100 


10      120  X  840  X  36  x  24-7 
16       62   x'60   X  60 


=  1-22 


Weight  per  week  in  ounces  =  1-22  x  \%  =  1-95 

Hanks  per  week  =  -ittt  x  -  -  =  14-62 
lb  1 


Dobson  Double  Speed  and  Hastening  Motion. — Fig.  35  shows  the 
arrangement  in  Dobson  and  Barlow's  fine  mules  for  driving  the 
spindles  at  two  speeds. 

A  and  B  are  drums  of  different  size  on  the  line  shaft ;  these 
are  connected  to  the  counter  shaft  by  belts  under  control  of 


Line  Shaft 


Counte 


Taking  in 
Motion  Shaft 


Fig.  35. 


forks  attached  to  the  same  bar.  The  stop  rod,  operating  the 
straps,  is  notched  to  occupy  the  three  positions  as  follows — 

(1)  Machine  stopped;  (2)  first  speed,  B  strap  driving; 
(3)  second  speed,  A  strap  driving. 

This  rod  is  operated  in  its  second  and  third  movements  by 
the  movement  outward  and  inward  of  the  carriage.  The  speed 
may  be  changed  from  the  second  to  the  third  at  any  point  in  the 
outward  run  of  the  carriage,  by  adjustments. 


AND  COSTS   OP  YARN 


191 


The  special  counter  shaft  has  provision  for  driving  the 
talang-in  motion  shaft  and  also  for  driving  the  rim  ""shaft. 
The  former  has  been  introduced  to  displace  the  friction  clutch, 
driving  the  taking-in  movement,  with  the  view  to  obtaining 
smoother  action.  The  latter  is  for  driving  the  rim  shaft  at  the 
closing  stages  of  each  draw,  and  to  secure  more  reliable  move- 


Back  Shaft 


Peg  release" ' 
wheel  for 
strap  dis- 
engagement 

Front 
Roller 


Click 
escapement 
Clutches 


Speed 
change  wheels 


20    i-Twist 
I— flpwheel 

^"•ix, 


I25  n-rrH 


Back  Shaft 
Scroll 


36 


Change  wheels 
'-'^Tor'gain 


B.R.W. 
1401  20 


90  i  , 

60  1401  - 


[4^ 


30 
F.R.  Clutch 


40 


16/ 
^20 


^^2 


Tin  roller 


shaft 


Fig.  36. 


^ 


ment  of  the  spindles  during  that  period  and  extending  durin.^ 
the  unlocking  of  the  fallers,  thereby  controlling  the  coils  wound 
upon  the  bare  spindle.  This  latter  action  is  that  commonly 
attributed  to  motions  described  as  "  hastening  motions." 

Piatt  Bros.  Jacking  Motion.— Figs.  36  and  °37  show  a  plan  of 


192 


COTTON   SPINNING  CALCULATIONS 


60 


Gain  Wheel - 


•Back  Shaft 


that  motion.    m{60  -  40)  and  a  (40  -  34)  are  compound  wheels 
loose  on  the  s^Dindle  NX,  and  they  are  driven  from  M  and  A  on 

the  front  roller.  M  is  loose 
on  the  front  roller  spindle, 
whilst  A  is  fastened  to  it. 
Movement  of  NX  is  therefore 
obtained  from  A  and  M,  one- 
half  being  expended  in  turning 
the  wheels  with  27  teeth,  upon 
their  axes,  and  causing  them 
to  roll  upon  the  two  34.  Thus 
one-half  of  any  motion  con- 
tributed to  a  or  m  passes  to 
the  T  arms  of  NX.  In  calcu- 
lating, the  formula  is — 


Gain  Bosswheel 

M36 
60,34^ 


34 


Fig.  37. 


2  2 

40  X  34 


U  = 


to    = 


40  X  34 
20  X  34 
60  X  34 


Thus,  with  the  front  roller  clutch  closed  and  making  100 
revolutions  per  minute,  the  rate  of  the  back  shaft  would  be — 


lOOt.2  (  45  X  36  \^(  100  X  1  ,  100  X  ^  A  1 
2V90X60/       V        2  2        ^2 


3 

2^5 


2         ■         2 
=  (66|)fo  =  20  revs,  per  minute 


If  the  front  roller  clutch  was  opened,  then  the  rate  would 
be- 

100f.2/'4o  X  36\      100  X  +      3       ^         ,   ..  •  „, 

-^(90^r6())  =  -^^  ^  To  =  ^  revolutions  per  mmute 


The  rate  of  the  carriage  during  the  jacking  is  thus  one-fourth 
the  normal,  and  in  addition  that  due  to  the  size  of  the  portion 
of  the  back  shaft  scroll  in  action. 


AND   COSTS   OF   YARN 


193 


To  find  the  revolutions  of  the  front  roller  when  the  revolu- 
tions of  the  back  shaft  are  3i  per  draw  of  62i-inch  draw : 
Let  X  =  revolutions  of  front  roller.     Then — 


X  X  40  X  S4:      X  X  20  \45  X 


*  V2      6ao        ■''    6 


36 


2  X  40  X  34  '  2  X  60^90  X  60  ~  "^^ 


19  X  10 


190  X  6 


eao      "•''6        5X3'   ■  ~    15  X  4 
.-.  a.'  =  -^:;^  =  19  revolutions  of  front  roller 

In  mules  not  arranged  with  this  motion,  the  gain  wheel  is 
driven  by  a  wheel  on  the  front  roller. 

In  Trelfall's  Jacking  Motion  (Fig.  38),  the  right  and  left  clutch 
wheels,  130  teeth,  are  loose  upon  the  shaft ;  the  central  portion 

36 


Back  Shaft 


13 


T- 

li5U-p— I 1-. 

't  i  o  11 -'"^^''''^''^^'^''^^'^'^^^ 


40 


130 
Jac 

mot 

Clutch     >  I    A    in 


130- 


SN\yV\f7V\NV^N'. 


70 


50- 


/ 


Gain'Wheel 


Rim  Shaft 


148 


50 
-I— 


70  \ 
(-„  Speed  change 
^^         wheel 


Rollec  motion 


48 


plw^^wwjwlvl  •": Clutch 


Front  roller  I 

Fig.  38. 

is  connected  to  the  shaft  upon  a  feathered  key  or  the  equivalent. 
The  clutch  is  now  shown  with  the  carriage  driven  at  the  normal 
rate.  The  movement  of  the  clutch  towards  the  back  shaft  to 
engage  the  other  130  part  of  this  clutch,  would  set  the  back  shaft 
moving  at  the  slowest  rate,  namely — 
53  X   70 


50  X  130 


=  normal  rate 


40  X   20       .    ,. 

7Q  ^  ]^3Q  =  jacking  rate 


=  f;:-  the  normal  =  6-5 


194  COTTON   SPINNING   CALCULATIONS 

The  Losses  in  Driving  in  Mules. — The  following  is  an  instance 
of  the  difference  between  the  calculated  and  actual  speeds  of  the 
parts  in  a  mule  when  the  former  were  made  without  allowances 
for  losses  arising  from  slippage  in  the  non-positive  gearing. 
The  revolutions  per  minute  of  the  line  shaft  was  235,  and  the 
connection  to  the  rim  shaft  and  spindles,  respectively,  fa  ^  i  It' 

17'^  X  6 

~i4 VT.     The  time  taken  to  draw  the  carriage  out  to  a  head 

111  X  f 

was  12j  sees. 

The  calculated  The  actual 

revolutions  in  revolutions  in  Loss 

drawing  the  drawing  out  per  cent, 

carriage  out.  the  carriage. 

Kim  shaft 17-2-5                 138         =         18-8 

Tin  roller 263                    211         =         24-0 

Spindle 1537  2100         =         26-8 

Percentage  of  slippage  in  driving  from  : 

The  rim  to  spindles 8*9 

The  rim  to  tin  roller 5*2 

The  tin  roller  to  the  spindles  .     .     .  3*93 

The  loss  shown  in  the  third  column  is  inclusive,  and  repre- 
sents the  extent  which  the  actual  differs  from  the  calculated. 

Deductions. — The  allowance  in  calculating  the  time  taken,  and 
the  speed,  during  twisting,  should  be  about  25  per  cent,  when 
the  conditions  are  normal. 

In  arranging  the  driving  gear,  from  3  to  5  per  cent,  should 
be  allowed  for  each  band  drive.  The  losses  noticed  in  belt 
drives  when  the  conditions  are  good — i.e.  rational  sizes  of  drums 
and  widths  of  pulleys,  and  when  not  reversing — are  only  very 
slight,  and  need  scarcely  be  taken  into  account. 

In  cases  of  very  high  speeds  the  losses  will  be  greater.  Con- 
siderable variation  existed  in  the  loss  recorded  at  different 
spindles,  most  probably  due  to  differences  in  their  resistance 
and  in  the  tension  of  their  bands. 

The  slippage  in  the  gear  between  the  rim  and  line  shaft  is 
only  slight  when  the  best  systems  are  adopted.  The  chief  loss 
is  that  due  to  reversing. 

Further  examples  of  loss  in  driving  mules  follow. 

Particulars  relating  to  the  Driving  of  the  Parts  in  Fig.  35, 
Dobson  and  Barlow's  Mule  for  Fine  Numbers. 


AND   COSTS   OF   YARN  I95 

Revolutions  of  the  line  shaft,  235  per  minute,  actual, 
Drums  on  the  line  shaft,  A,  32  inches  ;  B,  18  inches. 

Counter  Shafts.— The  principal  counter  shaft :  C,  20  inches  ; 
D,  20  inches  ;  G,  12  inches ;  E,  24  inches  diameter. 

The  auxiliary  counter  shaft:  H,  20  inches;  I,  9  inches; 
K,  15  inches  diameter. 

lUiii  Shaft.— Fast  and  loose  pulley,  F,  16  inches  ;  hasten 
motion  pulleys,  J,  15  inches;  rim  pulley,  16  inches  (12-22  inches), 
diameters. 

rahimj-in  and  Baching-off  Motion  Shaft  PuUrys.—L,  U  inches 
diameter. 

Sjnndles.— mm,  16  inches;  tin  roller  pulley,  10  inches;  tin 
rollers,  6  inches  ;  spindle  wharves,  |  inch  diameters. 
Eate  of  revolutions  per  minute  of  : — 
The  principal  counter  shaft — 

.    ,  ,    235  X  18 

first  speed,  ^ =  211-5 

second  speed,  ~~~  =  376 

^0 
The  auxiliary  counter  shaft — 

first  speed,  ?5^-2ii§^12^  126-9 
^      '  20  X  20        ^  ^ 

second  speed,  ?35_x_32j<jL2 

20  X  20      "^"^^  ^ 
The  rim  shaft— 

n    .  ,    235  X  18  X  24 

first  speed, g^  =  317-25 

second  speed,  ?35j^ll2ili  =  g.. 

Under  the  hastening  motion 

High  speed,  ^MA|2J<J^XJ^  ^ 

^  20  X  20  X  15      -^"^^ 

Low  speed,  235j<J^8j^l2  x  9  _ 

^       '  20  X  20  X  15  ~  ^^  "^ 

NoTE.-The  latter  are  successively  in  action  at  the  close  of  winding. 


196  COTTON   SPINNING   CALCULATIONS 

The  rates  of  rotation  per  minute  of  spindles — 

,,,  235  X  18  X  24  X  16  X  6       ,_„  „    ,  , 

^1)  20  X  16  X  10  Xl  =  ^^^^  ^''^  '^''''^ 

.„.  235  X  82  X  24  X  16  X  6      _„,„  ,  , 

(2)  20  X  16  X  10  X^  =  ^^^^  ^^^^^^  '^''^ 

.o,  235  X  82  X  12  X   9   X  16  X  6      i„oo  n   t  i,  i   ;i     • 

^^>  20  X  20  X  15  X  10  X  r  ^T^    "^^  speed  during 

the  action  ol  the  hasten- 
ing motion 

,,  285  X  18  X  12  X   9   X  16  X  6        ^„ ^  a  ■,  ^  ;■-.* 

^^>  'l    X20X^X15X10X^  =    ^^^'^  ^"^  'P^'^  ^^**°- 


The  Losses  in  Driving. — Under  the  above  conditions  in  respect 
of  the  gear  the  actual  rates  of  the  spindles  were  observed  to  be 
less  to  the  extent  of :  (1)  225  per  cent. ;  (2)  23-5  per  cent. ; 
(3)  18*75  per  cent. ;  (4)  11*15  per  cent. 

Further,  the  twist  wheel  contained  72  teeth,  and  moved  2 
revolutions  per  draw;  during  twisting  the  movement  was 
140  teeth,  and  the  revolutions  of  the  spindle,  in  the  correspond- 
ing period,  1454.  This  shows  a  loss  of  18*8  per  cent.,  the 
calculated  speed  being  as  follows  : — 

1-^0  X  16  X  6  _ 

icr>u  ~ 

or  388  revolutions  of  the  spindles  more  than  the  actual. 

The  time  occupied  in  making  this  movement  was  12i  seconds 
at  first  speed,  and  8^  seconds  at  second  speed,  in  these  periods 
the  actual  revolutions  of  the  spindles  being,  respectively,  672 
and  782. 

These  speeds  represent,  resjDectively,  the  following  average 
rates  per  minute  : — 

672x60      „,_        ,782x60_.„^„ 
— TTri —  =  3150,  and  — ^^^ —  =  5520 
Iz*  o'5 

The  loss  of  time  by  the  rim  shaft,  as  indicated  by  the  above 
speeds,  is  therefore  as  follows — 


AND   COSTS   OF   YARN  197 

Calculated  revs,  of  rim  shaft  in    8i  sees,  at  second  speed  =  80-0 
"  >'  »    121       „       first  „     =  67-5 

147-5 

Thus,  140  revolutions  require  the  time  of  147-5,  or  time  lost 
by  the  rim  shaft  =  S'OS  per  cent. 

_  From  this  it  is  seen  that  5-08  per  cent,  of  the  18-8  per  cent. 
IS  between  the  rim  and  the  driving  shafts,  the  major  portion, 
Id  per  cent.,  being  between  the  spindles  and  rim  shaft. 

Twist    per    Iiich._The    length    wound    per    draw    was    as 
lollows : — 

Distance  moved  by  the  carriage  each  draw  =  59-5" 

Length  del.  by  F.R.  during  the  run-in  of  the  carriage  =    4-5" 

The  approximate  length  wound  =  64-0" 

Actual  twist  per  inch  =  ^^  =  22-7 
Calculated  twist  per  inch  =  ^H^  =  28 

The  actual  count  spun   was  60^  so  that  the  actual  twist 
22-7 
co-efficient  =  ^  =  2-93,  as  against  3-62  calculated. 

The  front  roller  made  the  following  movements  each  draw  :- 

(1)  During  the  engagement  of  the  F.R.  clutch,  ]      ,  ,  ,„ 

164  revolutions  =  o4-6 

(2)  During  the  jacking  and  twisting  at  the  head  ) 

actions,  1^  revolution  =    1 

(3)  During  the  inward  run  of   the    carriage  ) 

1  revolution  (        '^'^" 

Total  length  delivered  per  complete  draw    =  60-0" 
Length  wound  per  draw  =  64" 

The  total  stretching  of  the  yarn  per  draw  is,  therefore, 
64  -  60  =  4  inches.  Of  this,  the  amounts  obtained  during  the 
above-named  periods  are — 


198  COTTOX   SPINNING  CALCULATIONS 

(1)  the  movement  of  the  carriage  being  56"  =  56"  — 54*6,  =1'4 

(2)  „  „  „  3i"  =  3r-l,        =2^ 

3-9 

Length  not  accounted  for  =0*1 

4-0 

The  actual  revolutions  of  the  rim  shaft  after  the  disengage- 
ment of  the  F.E.  clutch,  i.e.  during  jacking  and  twisting  at  the 
head,  were  73.  Therefore  the  length  which  should  be  dehvered 
by  the  F.E.  during  this  period,  by  reason  of  the  action  of  the 
slow  roller  turning  motion,  is  : 

^  73  X  19J<  20  X   1    X  24  X  1,V  X  22  ^  .^^^^^ 

58  X  40  X  30  X  24  X    7 

The  actual  length  observed  was  1  inch.  The  difference  was 
undoubtedly  due  to  the  backlash  in  the  motion. 

Note. — The  difference  noted  in  the  actual  and  calculated  rates  of  the  spindle 
emphasize  the  importance  of  not  relying  on  the  calculated  revolutions  of  tlie 
spindle  unless  due  allowances  have  been  made  for  slippage  in  the  belt  and  band- 
driving  gears.  The  use  of  a  tachometer  is  very  helpful  when  arranging  the 
gearing.  The  particulars  given  were  ascertained,  accurately  and  expeditiously, 
by  the  aid  of  that  instrument. 


Speed  Indicators. 

Losses  in  the  Transmission  of  Motion,  and  how  Ascertained. — 

The  most  convenient  mode  of  ascertaining  the  extent  of  losses 
arising  in  the  transmission  of  motion  is  by  the  aid  of  a  self 
time -registering  tachometer.  The  ordinary  tachometer  is  defective 
in  that  the  attachments  for  connections  are  imperfect,  and  in 
addition  the  timing  has  to  be  done  either  by  a  second  person 
or  the  attentions  of  the  operator  divided  between  the  timepiece 
and  the  tachometer^  In  either  case  the  work  is  not  altogether 
satisfactory. 


The  illustration  (Fig.  39)  is  of  a  tachometer,  and  suitable 
attachments  for  spinning  machinery.     It  consists  of  a  recording 


AND   COSTS    OF   YARN  199 

timepiece,  D,  with  minutes  and  seconds  dials  combined  on  the 


II 
4  * 


m 


D 

Fig.  39. 


left   hand.     This  is  fitted  ^Yith  a  fly-back  action.     The  timincr 


200  COTTON   SPINNING  CALCULATIONS 

commences  upon  pressure  being  applied  to  the  recording 
spindle  2,  the  centre  finger  recording  from  I  to  60  seconds, 
and  the  lower  finger  the  minutes.  The  lower  projecting  milled 
head  is  for  setting  back  the  minutes  finger,  and  the  slight 
projection  on  the  left  hand  is  the  fly-back  release  for  the 
seconds.  The  large  right-hand  deal  finger  indicates  the 
revolutions  up  to  100,  and  the  small  one  on  the  inner  left 
the  hundreds,  whilst  that  on  the  inner  right  records  the 
thousands.  The  projection  on  the  underside  of  the  right  dial 
is  the  fly-back  release  for  the  unit-tens  finger,  the  hundreds 
and  thousands  fingers  being  reset  by  means  of  milled  heads  at 
the  back. 

F,  H,  are  rubber  cupped  detachable  ends  for  the  spindle  of 
the  tachometer. 

E,  and  that  on  the  left  of  centre  are  rubber  pivoted  detach- 
able ends  for  the  spindle  of  the  tachometer. 

That  on  the  right  of  centre  is  a  pyramidal  recessed  end  for 
the  spindle  of  the  tachometer. 

J,  K  are  pyramidal  ends  for  fitting  to  mule  and  ring  spindles 
for  use  in  connection  with  those  found  on  the  left  and  right  of 
centre. 

This  instrument  is  held  by  the  detachable  handle  D.  In 
use  its  great  feature  is  that  it  can  be  held  in  one  hand,  and 
with  this  exception  the  whole  of  the  attentions  of  the  operator 
are  available  for  other  work  throughout  the  observations.  The 
dials  record  the  results,  the  range  of  speed  being  up  to  10,000 
revolutions  per  minute. 

Length  and  Hank  iNDicATOPtS. 

Fig.  40  shows  the  gearing  in  an  indicator  for  registering  the 
number  of  draws  in  mules.  The  segmental  wheel  is  driven  by 
a  worm  placed  upon  the  back  shaft  of  the  mule  (drawing-out 
shaft).  The  sector  lever,  b — hi,  secured  to  a,  operates  the  star 
wheel  c ;  to  the  latter  a  3-treaded  worm  is  secured,  and  this 
drives  the  worm  wheel  d  on  the  spindle  ch — f/2.  Five  dial  discs  are 
mounted  on  this  spindle,  and  these  record  units,  tens,  hundreds, 
thousands,  and  tens  of  thousands  respectively.     Each  of  these 


AND   COSTS   OF   YAEN 


201 


are  connected,  in  sequence,  by  a  train  1  driving  a  4,  the  latter 
being  compounded  with  an  8,  which  drives  the  20  secured  to  the 
next  dial.  The  first  dial  is  secured  to  di — d2,  and  the  rest  are 
free  upon  it.     Thus  this  instrument  records  from  0  to  99999 


20,       20,  20,         20. 

8,         8,  8,  8, 

,4,  4.  4,  4. 


Fig.  40. 


draws,  the  object  being  to  record  the  work  done  in  a  given  time 
for  estimating  the  earnings  and  for  other  purposes. 

The  record  is  exact,  as  shown  by  calculation.     Thus — 


20  X  4  X  20  X  4  X  20  X  4  X  20  X  4  X  10  X  3 
8x1x8x1x8x1x8x1x3x1 


=  100,000  hanks 


recorded  on  the  dials  by  its  moving  from  00000  to  99999,  and 
then  00000,  or  one  complete  revolution  of  the  left-hand  dial. 


Fig.  41  shows  the  gearing  in  a  hank  indicator  as  used  in 
mules.  These  instruments  are  arranged  to  record  the  production 
of  the  whole  of  the  spindles  in  the  machine,  and  hence  the  gear 
is  varied  to  adapt  them  for  the  different  numbers  of  spindles 
which  the  mules  contain  and  the  length  of  the  draw.  In  the 
figure  the  particulars  are  of  one  designed  for  a  mule  containing 


202 


COTTON   SPINNING   CALCULATIONS 


184  spindles  only,  and  making  a  draw  of  58^  inches.  It  records 
from  0  up  to  20,000  banks,  the  customary  allowance  for  loss 
through  breakages  being  2^  per  cent.  The  action  in  this  case 
is  as  follows  : — 

a,  rti,  a-j,  03,  cii  are  attached,  this  part  is  actuated  by  a  worm, 
X,  placed  upon  the  back  shaft.  By  that  means  a,  ai,  a^, 
oscillate,  each  draw,  and  the  sector  lever  a^a^^  moves  the  star 
wheel  h  one  tooth,      h  is  compounded  with  c,  30;  this  latter 


Fig.  4L 


drives  cl,  the  15.  d  is  compounded  with  the  worm  c  (1),  which 
drives  j-  (20).  f  is  compounded  with  the  single  worm  g,  and  the 
latter  drives  h.  The  lever  i,  i,  is  fastened  upon  the  axle  of  h, 
and  this  is  loose  on  the  central  spindle.  At  the  extremity  of 
this  lever  is  the  wheel  21,  mounted  free  on  a  stud,  and  its  teeth 
engage  two  wheels,  JcS9  and  /40  respectively,  k  being  secured 
and  cannot  rotate.  /,  being  free,  is  moved  one  tooth  per  revolu- 
tion of  the  lever  /,  /,  upon  its  centre.     The  index  finger  ki  is 


AND   COSTS    OF   YARN  203 

attached  to  I,  and  this  moves  in  front  of  the  dial  indicating  from 
0  to  20,000  hanks. 

The  length  of  yarn  made,  per  184  spindles  winding 
58^  inches  per  draw  and  assuming  no  loss,  per  20,000  hanks 
registered, 


_  40  X  48  X  20  X  15  X  8  X  184  X  58V' 
-    1    X    1    X    1    X  30  X  1  X  840  X    36 

NoTK. — 512  hanks  =  2^-  per  cent. 


=  20,503  hanks 


Exercise  1. — A  mule  containing  796  spindles  and  winding  G7  inches  per 
draw  has  the  following  wheels  stamped  upon  it,  IG  x  6  x  3  x  41,  and  it  indicates 
20,000  hanks  per  draw.     What  percentage  does  it  allow  for  breakage  ? 

Ans.  3'9G,  or  1'4G  in  excess. 

Exercise  2.— For  what  number  of  spindles  per  mule  would  the  following 

20  20  21    15  3 
hank  indicators  be  adopted  ?     Particulars  of  their  gear,  y'  ^'  y'  on'  ^'  assum- 
ing the  length  wound  per  draw  68  inches,  and  the  indicator  to  record  up  to  20,000 
hanks.  Ans.  G8G. 

Exercise  3. — What  number  of  hanks  must  be  recorded  per  draw  by  the 
hank  indicator  in  a  mule  containing  1200  spindles  and  winding  64  +  4  inches 
per  draw,  if  2i  per  cent,  is  allowed  for  breaknge  ?  Ans.  2*63. 

Exercise  4. — What  alteration  in  the  value  of  the  following  underhned 
portions  of  the  gear  in  an  indicator  would  adapt  it  for  a  mule  of  1200  spindles, 
making  a  64-inch  draw  and  4  inches  inward  roller  delivery,  allowing  2^  for  loss? 

,,  ,        ^^,  20   20   21    15   3 

Value  of  the  gear,  y,  ^  ,   j,  ^,  ^■ 

A71S.  Present  value  of  the  train  =  12.600,  or  number  of  draws  to  move  the 
dial  one  revolution. 

Piequired  value  of  the  train  =  7601,  or  number  of  draws  to  move  the 
dial  one  revolution. 

Value  of  the  gear  required  =  ;5 — ^  =  5067 
oX^ 


204 


COTTON   SPINNING  CALCULATIONS 
Productions  ix  Mules. 


Production  iu 

Production  in 

Production  in 

Production  in 

hanks  per  spindle 

hanks  per  spindle 

hanks  per  spindle 

hanks  per  spindle 

Count. 

per  55i  hours 

per  55  hours 

Count 

per  55  f  hours 

per  55  hours 

inclusive. 

inclusive. 

iLclusive. 

inclusive. 

Twist. 

Weft. 

Twist. 

Weft. 

16^-28 

32-35 

30-34 

61 '-80 

16-75-19-75 

17-20-5 

30 

31-33 

31-33 

82 

16-5-19-5 

— 

32 

29-32 

30-32 

84 

15-75-19-25 

— 

34 

28-31 

29-31  2 

86 

15-5-19 

16-5--20 

36 

27-5-30-8 

28-5-31 

88 

15-25-18-8 

. 

38 

27-30 

28-30-75 

90 

15-1-18-6 

16-19-7 

40 

26-5-29-5 

27-29-5 

92 

14-9-18-4 

— 

42 

26-29 

26-5-29 

94 

14-8-18  1 

— 

44 

25-5-2S-5 

26-28-5 

96 

14-6-17-75 

15-5-19-3 

46 

25-28 

25-28 

98 

14-4-17-5 



48 

24-5-27-5 

24-5-27-5 

100 

14-2-17-25 

15-19 

50 

24-27 

24-27 

110 

14-17 

15-18-5 

52 

23-5-26-5 

23-5-26-5 

120 

13-7-165 

14-1725 

54 

23-26 

23-26 

130 

13-3-155 

13-5-16 

56 

22-5-25-5 

22-5-25-5 

140 

13-14-25 



58 

22-25 

22-25 

150 

12-26-14 

— 

60 

21  •5-24-5 

22-5-26-5 

160 

12-13 

— . 

62 

21-23-5 

22-26 

170 

11-12 



64 

20-22-5 

21 -5-25-6 

180 

10-11 



66 

19-5-22 

21-24-8 

190 

9-5-10-5 



68 

19-21-5 

20-24 

200 

9-10 



70 

18-5-21-25 

19-5-23-2 

240 

7-2-8-2 



72 

18-21 

19-22-8 

260 

6-4-7-4 



74 

17-5-20-5 

— 

280 

5-6-6-6 



76 

17-25-20-25 

18-21-9 

300 

4-9-5-9 



78 

17-20 

— 

The  Ring  Frame.— Figs.  42  and  43  represent  the  gearing 
common  iu  ring  frames. 

A  =  The  back  roller  and  its  wheel  for  driving  that  on  the 
middle  roller. 

B  =  The  carrier  wheel  connecting  the  back  and  the  middle 
rollers. 

C  =  The  wheel  upon  the  middle  roller. 

D  =  The  draft  change  wheel  on  the  back  roller. 

E  =  The  draft  change  pinion  driving  the  back  roller  wheel. 

F  =  The  crown  wheel  compounded  with  the  draft  change 
pinion  and  gearing  with  the  front  roller  wheel. 

G  =  The  wheel  on  the  front  roller  for  driving  the  above  gear. 

H  =  The  wheel  on  the  front  roller  gearing  with  the  train 
I,  J,  and  K. 


AND   COSTS   OF   YARN 


205 


K  =  The  twist  change  wheel. 

L  =  The  twist  stud  wheel,  and  MN  the  connecting  train 
from  the  tin  roller  shaft. 

N  =  The  tin  roller  shaft  wheel,  this  is  changed  when  an 
extension  in  the  range  of  the  twist  is  desired  beyond  that 
procurable  by  altering  the  twist  wheel. 

P,  Pi  =  The  tin  rollers  driving  the  spindle  bands. 

Q  =  The  spindle  wharve.  The  spindles  are  arranged  in 
rows  on  either  side.  The  band  indicated  by  the  dotted  lines 
shows  the  driving  when  double  tin  rollers  are  used  for  one 
side  only. 

Fig.  43  shows  the  driving  of  the  cam  W  for  reciprocating 


Fig.  42. 


m 

V 


Fig.  43. 


W 


the  ring  rail,  the  rate  at  which  this  is  driven  controls  the  pitch 
of  the  coils  contained  by  the  bobbin. 

S,  T,  U,  V,  are  the  train  of  wheels  connecting  W  with  I.  W 
produces  the  reciprocation  of  the  ring  rail  through  the  medium 
of  a  series  of  levers,  rods  and  chain  connections.  The  relative 
positions  of  their  movement  is  advanced  through  the  agency 
of  a  ratchet  wheel  and  a  pawl,  the  ratchet  wheel  being  termed 
the  builder  wheel. 

The  number  of  teeth  in  the  builder  wheel  and  the  value  of 
its  driving  train,  S,  T,  U,  V,  control  the  length,  and  therefore 


206  COTTON    SPINXIXG   CALCULATIONS 

the  weight  of  yarn  placed  upon  the  bobbins.  When  the  rate 
of  reciprocation  is  insufficient,  and  other  means  have  been 
exhausted,  the  speed  of  this  part  is  changed  by  introducing  a 
single,  double,  or  a  treble  worm  at  T.  The  movement  of  the 
pawl  operating  the  ratchet  is  adjustable  to  the  extent  of  the 
var3ang  sizes  of  the  teeth  in  the  builder  wheels  applicable. 

D,  E,  F,  G,  are  the  gear  for  driving  the  rollers  on  the  right- 
hand  side,  and  these  are  a  duplicate  of  those  on  the  left  side. 

Pi,  is  the  driving  pulley  connected  by  belt  or  rope  with  the 
line  shaft. 

The  speeds  of  the  spindles  in  these  machines  usually  range 
from  6000  to  11,000  per  minute,  actual.  The  usual  sizes  of 
rollers  are  from  I  to  1,^  inch  for  the  front  and  back  positions, 
and  I  less  for  the  middle  roller ;  ^  inch  is  used  for  short  and 
1^  inch  for  long-stapled  cottons. 

The  recognized  twist  for  ring  yarns  is  4\/count  per  inch. 
This  is  not  rigidly  adhered  to,  exceptions  being  made  when 
it  secures  better  spinning  and  the  amount  of  the  twist  has  not 
been  stipulated. 

The  Speeds  of  Spindles. — The  circumstances  that  govern  the 
best  speeds  of  the  spindles  are  :  quality  and  count  of  the  roving 
and  yarn  ;  condition  of  the  machine  ;  expertness  of  the  workers. 
Under  the  most  favourable  conditions,  a  speed  of  10,500  revo- 
lutions actual  may  be  attained  with  counts  30'-36'.  For  other 
counts,  under  the  best  conditions,  the  following  revolutions  per 
minute  of  spindle  are  given  as  a  guide : — 

For  counts  below  30^ — 

10000\/intended  count 

VBO 
For  counts  above  36* — 

lOOOOv/36 


^/intended  count 
When  the  conditions  are  identical  but  not  satisfactory  for  the 
above : 

For  counts  below  36* — 


known  satisfactory  speed  X  i/'intended  count 
\/count 


875 


AND   COSTS    OF   YAl^N  207 

For  counts  above  36^ — 

known  satisfactory  speed  X  v^count 
-^/intended  count 
With  the  largest  and  smallest  sizes  of  the  twist  change  wheels 
given  in  Fig.  -42,  and  the  spindles  making  10,000  revolutions 
per  minute,  the  speed  of  the  parts  would  be  as  follows  : — 

Parts.  AVith  the  smallest  change  wheels.  ^^5'^  "^®  largest 

"  change  wheels. 

Tin  roller  shaft  and  )  10000  x  ^  _      . 

machine  pulley     f 10         ~ 

,.      ,     1,                           10000  X   I  X   25   X  25      ._  .,.-,0 

1  rent  rollers    .... l(rx-T2T^80  =  ^^  ^"^ 

"With  rollers  of  the  following  diameters,  the  lengths  delivered 
per  minute  respectively  are — 

Parts.  With  the  smallest  change  wheels.  Yhfnge  wS" 

T3    X'      .     „       7»  J-       .            57  X  ^  x  22       ,  _„         228  x  Z-  x  22      ^.^„ 
by  iront  roller,  ^    diameter    .     ^ ^  =  lo< ^  =  628 

By  front  roller,  1^"  diameter  .  203"  812" 

The  twist  per  inch  under  the  above  conditions  would  there- 
fore be — 

Parts.  With  the  smallest  change  wheels.  ^h'ange  wS.' 

By  front  roller,  |"  diameter      .     .     .    ia§ao  ^  (53.7  iaa|<i  =  15-9 

By  front  roller,  l^"  diameter    .     .     .    Hggfi  =  49-2  itt'l^Q  =  12-3 

Thus  the  twist,  with  the  sizes  of  change  wheel  applicable 
and  the  front  roller  ^  inch  in  diameter,  ranges  from  15"9  to  63'7 
turns  per  inch  of  yarn  delivered  by  the  front  roller. 

This  calculation  is  based  on  the  twist  being  equal  to  the 
revolutions  of  the  bobbin.  This  is  inaccurate  when  the  yarn  is 
unwound  from  the  side  of  the  bobbin,  but  correct  when  the  yarn 
is  unwound  from  the  ends  of  the  bobbins.  To  arrive  at  the 
actual  twist  inserted  during  spinning,  it  is  necessary  to  deduct 
from  the  revolutions  of  the  bobbin,  the  revolutions  about  the 
bobbin  made  by  the  yarn  in  obtaining  winding. 

The  different  sizes  of  the  twist  wheels  applicable  w'ould 
therefore  obtain  the  following  amounts  of  twist  when  the  tin 


208  COTTON  SPINNING  CALCULATIONS 


roller    wheel    is     25     and    the     front     roller    is 

I-    inch    in 

diameter  :  — 

Size  of  twist  wheel     25      26      27       28      29      30  ...  35  .  , 

,.  40  ...  45 

Twist  per  inch .     .63-7     61-2   59-0   56-8   54-9   53-0  ...  45-5  .  . 

.  39-8  .  .  .  35-3 

Size  of  twist  wheel    46         47        48        49        50 

Twist  per  inch .     .34-6       33-9      33-2     32-5     31-8 

The  above  are  ascertained  in  the  following  manner  : — 
Eevolutions  of  spindle  per  inch  delivered  by  the  front  roller 

80    .,     120     ^  10"  ^        1 


T.W.      T.R.W.       I" 


and  hence  with  a  25  tin  roller  wheel,  and  a  50  twist  wheel,  the 
revolutions  of  the  spindle  per  inch  delivered  by  the  front  roller 

_80      120      10  1       _ 

-25^  59   ^I^r^-^-^^^ 

These  results  may  also  be  ascertained  as  follows  : — Assuming 
that  the  tin  roller  wheel  was  25,  and  the  twist  wheel  contained 
only  one  tooth,  the  twist  per  inch  would  be  63'7  X  25.  (This 
is  called  the  twist  change  wheel  constant  number  for  a  25  tin 
roller  wheel,  and  the  front  roller  I  inch  in  diameter.) 

63'7  X  25 
.*.    — ^7, =  the  twist  per  inch  when  a  26  wheel  is  used 

T.W.  constant      ,,     ,    .  ,  .     , 

oi'j  ^~. — j-T — i — -1  =  the  twist  per  mch 
mtended  wheel  ^ 

T.W.  constant  •     i     ,     i 

.'.  ■    ■  , -. — r  =  required  wheel 

twist  per  inch         ^ 

When  the  limit  in  the  range  of  sizes  of  twist  wheels  is  reached, 
they  may  be  rendered  again  available  by  altering  the  size  of 
the  tin  roller  wheel,  in  the  proportion  which  the  range  of 
wheels  represent.  The  limit  in  the  present  instance  is  reached, 
with  a  25  tin  roller  wheel,  when  the  twist  wheel  is  50,  the  twist 
in  the  yarn  is  31-8  per  inch.  By  adopting  the  size  of  tin 
roller  wheel  that,  together  with  a  25  twist  wheel,  will  produce 
31 '8  twists  per  inch,  the  range  of  twist  wheels  are  again  avail- 
able.    Thus — 


AND   COSTS   OF   YARN  209 

63*7  X  25  =  the  tin  roller  change  wheel  constant  number  for 
a  twist  change  wheel  of  25  teeth 

.-.  — ^^  „ —  =  the  required  tin  roller  wheel  =  50 

and,  therefore,  with  a  50  tin  roller  wheel,  and  with  the 
stated  range  of  t\Yist  wheels,  the  following  twists  will  be 
obtained ; — 

Size  of  twist  wheel    25       26       27  .  .  .  30  .  .  .  34       35  .  .   .  40  ...  45 
Twist  per  inch .     .   31-8     306     29-4.  .  .26-5.  .  .23-4    22-9.  .  .19-8.  .  .17-6 

Size  of  twist  wheel     46        47        48        49        50 
Twist  per  inch .     .    17-3     169     16-5     16-2     15-9 

Twist  change  wheels  are  usually  drivers  in  the  train  to  the 
front  rollers,  and  therefore  increasing  their  size  increases  the 
length  of  yarn  submitted  for  twist  in  direct  proportion,  and 
hence  the  twist  is  reduced  inversely. 

To  change  the  Counts. — This  is  done  in  the  same  way  as  in 
the  previous  machines — 

(a)  By  altering  that  of  the  feed. 

(b)  By  altering  the  extent  of  the  attenuation  or  draft. 

The  results  are  directly  proportional  to  alterations  in  either 

case.     Thus  : 

the  weight  unit  of  the  feed      ,,         .,.       ..    f,,     ,,. 
, ,  ... =  the  weight  unit  oi  the  delivery, 

and  vice  versa 

the  count  of  the  feed  x  the  draft  =  that  of  the  delivery,  and  vice 

versa 

The  draft  is  also  determined  in  the  same  manner.  Assuming, 
the  smallest  driver,  and  the  largest  driven,  of  the  draft  change 
wheels  are  used,  and  the  back  and  front  rollers  alike  in  size, 
then — 

the  draft  =  §|]  X  \Pf  =  10 

Hence,  with  the  back  roller  wheel  60,  the  range  of  pinions, 
applicable,  would  produce  the  following  drafts  : — 

Draft  pinion     30        31 
Draft.    .    .  10-0     9-65 


Draft  pinion     56        57        58 
Draft.     .     .    5-35     5-26      5-17 


32 

33 

34 

35  .  . 

,  .  40  . 

.  .  50  . 

.  .  55 

9-37 

9-1 

8-82 

8-57 .  . 

.  7-5  .  . 

.  .  6-0  . 

.  .  5-45 

58 

59 

60 

5-17 

5-08 

5-0 

210  COTTON   SPINNING  CALCULATIONS 

It  is  thus  seen  that  the  fractional  change  in  the  draft 
corresponds  with  the  fractional  change  in  the  wheel,  and  hence 
large  wheels  command  a  finer  adjustment  of  the  count, 
and  for  this  reason  the  use  of  small  change  wheels  should  be 
avoided  as  far  as  practicable. 

Whenever  the  size  of  pinion  required  is  not  available,  alter 
the  back  roller  wheel  in  the  inverse  proportion,  or  change 
the  back  roller  wheel,  altering  its  size  to  the  extent  that  will 
enable  the  use  of  the  available  wheels,  as  pinions.  The  following 
is  then  the  procedure  : — 

Ratio  of  pinion  and  back  roller  wheels,  -^.  ^-' — '- ;  and  any 
^  pmion 

two  wheels  which  give  a  near  enough  ratio  will  be  satisfactory. 

Always  remember  that  the  back  roller  wheel  has  the  inverse 
effect  to  the  pinion,  the  former  affecting  the  draft  in  the  direct 
ratio  and  the  latter  inversely. 

The  Builder  Wheel  (Ratchet). — In  changing  the  count,  the 

weight  of  the  yarn  is  affected  in  the  inverse  proportion,  so  that  if 

the  bobbins  are  required  to  contain  the  same  weight,  then  the 

ratchet  wheel  must  be  changed  in  direct  proportion  to  the  count. 

This  is  not  always  admissible  in   practice  on  account   of  the 

bobbins  being  filled  too  full  for  the  rings,  through  the  yarn  not 

being  wound  sufficiently  compact.     The  rule  in  calculating  the 

builder  wheel  is — 

Builder  wheel  X  count  required         ,      ,      .,  , , 

, =  wheel  suitable 

count  spun 

When  the   size  of  the   empty  bobbins   are    changed  or   a 

different  size  of  full  bobbin  is  required,  the  wheel   should  be 

altered  in  direct  proportion   to  the  area  of  the   cross-section 

of  the  yarn  contained  on  the  full  bobbin. 

The  relative  area  of  a  cross-section  of  the  yarn  =  (diameter 

of  full  bobbin  —  diameter  of  empty  bobbin)^. 

the  wheel  X  area  of  section  of  yarn  on  bobbin  required 

area  of  section  of  yarn  on  present  bobbin 

When  the  bobbins  are  insufficiently  hard,  and  the  traveller 
is  the  heaviest  practicable,  speeding  up  the  traverse  of  the  ring 
rail  by  the  most  convenient  of  the  wheels  S,  T,  U,  Y,  will  have 
a  beneficial  effect. 


AND   COSTS    OF   YARN 


211 


Exercises  is  chaxging  the  Counts  .vnd  otukii  Coxditioxs  of  Spixxixg  in 
THE  RiXG  Frame  (Fig.  42).  The  Froxt  axd  Back  Rollers  are 
takex  at  I  Ixcn  in  Diameter. 


EzerciEe  numbers. 


(1)  Count    of    tlie^ 

yarn  | 

(2)  Count    of    thel 

rove  / 

(3)  Rove,   whether 

single  or 

double 

(4)  Draft    .     .     . 
(.")j  Draft   wlieels  — 

F.R.W.  .  . 
C.W.  .  .  , 
P.W.  .  .  . 
B.R.W.  .  , 
(G)  Twist  per  inch  . 

(7)  Twist  wheels — 

T.R.W.     .     . 
T.W.    .     .     . 

(8)  Twist    change! 

wheels  con- 1 
staut  number  ) 
(;»)  Revolutions  otj 
spindles  per  j 
minute  ) 

(10)  Size  of  empty) 

and  full  bob- 
bins j 

(11)  Builder  wheel  , 

(12)  Hanks         pro-^ 

duced   per  10 
hours  (no 

allowances)     J 


37-5 


21 

105 

40 

60 


50 

? 

79.-) 


10,000 
f "  and 

13" 
-la 


40 
10 


21 

105 

? 

60 
25-3 

50 
? 

795 


50 

2 

10 

21 
105 

? 

60 
? 

25 


60 
15 


21 

105 

? 

60 
31 

25 


80 
20 


21 
105 

•? 

57 
? 

25 

9 


9500     9000     8500     8000 


30 
? 


21 
105 
ratio 

9 


50 

? 


20 
3^ 


21 

105 

40 

17-9 

50 

9 


10,500     9000 


f "  and 
U" 


— 

1"  and 
k" 

f "  and 

•? 

? 

0 

? 

? 

? 

? 

? 

16 
? 

1 
5-3 

21 
105 
ratio 

? 


50 

9 


8000 

f'and 

If 

? 

9 


Axswers  to  Exercises. 


Number  of  Exercise. 

Particulars. 

1 

2 

3 

4       ,       S 

6 

7 

8 

No.  1     .     . 

_  1     _ 

_     1     _ 

_ 

_ 

•} 

10 

— 

10 

—           — 

5 

— 

;{ 

„    4     .     . 

75 

8 



8 

8 

— 

5-72 



„    5     .     . 

.       — 

35 

30 

35 

35 

P.  5 
B.R.W.  6 

46 

P.  50 
B.R.W.  53 

„    6     .     . 

.     24-5 



28-3 



35-8 

21-9 

— 

16 

„    7     .     . 

.    32-4 

31-4 

56-2 

51 

44-5 

36 

44 

50 

„     8     .     . 





1590 

1590 

1590 

795 

795 

795 

„     11   .     . 

— 

38 

48 

58 

49 

41-5 

27-6 

30 

.,    12  .     . 

.      81 

7-46 

6-33 

5-45 

4-45 

95 

10-3 

16-6 

212  COTTON    SPINNING   CALCULATIONS 

EXASIPLES   IX   THE   WoKKIXG   OF   TUE    ExERCISES   OX   PagE   211. 

37.5  v^  2 

Exercise   1. — The  draft  =  fg  ^  W"!    ^^^^  count  of  the  rove  =     j    r.     ^ 

795 

the   twist  per   inch  =  4  V count ;    twist   wheel  = ;    the    hanks    pro- 

,       ,      revolutions  of  F.R.  per  10  hours  x  circle  of  F.R. 

duced  = -. — r T — 1 

inches  per  hank 

40 
Exercise  2. — The  draft  =  j-j~  =  8  ;  the  pinion  wheel  (a)  is  contained  in  this 

,.      60      105      o      .1      /•  ^      11      795  .      ,,      .  ,,      . 

equation  —  x  -^  =  8 ;    the   twist  wheel  =  ^^.^,   or,   as   x    in   the   following 

,.        80       120       10             1  or:  a      .1      1     -n  i      i       36  X  40     „„  , 

equation,  ^  x  -^  x  ^  x  j ^  =  25*3 ;  the  builder  wheel  =  —  =38-4. 

Losses  in  driving  the  Spindles  in  Ring  Frames. — The  following 
are  instances  of  the  observed  and  calculated  speeds  of  the 
spindles,  together  with  the  losses  arising  from  slippage : — 

King  frame  with  two  tin  rollers,  one  of  these  being  fixed  to 
the  machine  shaft,  and  the  other  driven  by  the  spindle  bands. 

Driver  T.R.  side.        Driven  T.R.  side. 

Actual  revolutions  of  T.R 565                      555 

Actual  revolutions  of  spindle     ....  6250  6824 

Calculated  revolutions  of  spindle   .     .     .  6460  6342 

Percentage  of  loss 3*25  8*1 

The  following  were  recorded  after  rebanding  the  spindles  on 
the  driven  tin  roller  side,  these  bands  being  driven  by  the  driver 
tin  roller  : — 

Driver  T.R.  side.        Driven  T.R.  side. 

Actual  revolutions  of  T.R 570  5G2 

Actual  revolutions  of  spindle     ....  6026  6020 

Calculated  revolutions  of  spindle   .     .     .  6541  6422 

Percentage  of  loss 6"67  7*5 

The  following  were  recorded  in  a  frame  having"  the  tin 
rollers  connected  by  an  endless  rope  drive  : — 

Driver  side.  Driven  side. 

Actual  revolutions  of  T.R 658  650 

Actual  revolutions  of  spindle     ....  7184  7065 

Calculated  revolutions  of  spindle    .     .     .  7500  7430 

Percentage  of  loss 4*2  4*7 

The  productions  in  ring  frames  vary  considerably,  depending 


AND   COSTS   OF   YAllN 


213 


upon  the  speed  of  spindles,  twist  per  iiicli,^  strength  of  tlie  yarn, 
skill  of  the  operatives  and  their  management. 

The  spindles  are  run  at  rates  as  high  as  11,000  revolutions 
per  minute,  this  being  exceptionally  high,  and  only  practicable 
under  the  most  favourable  conditions.  The  production  ranges 
as  high  as  96  per  cent,  of  the  calculated  when  based  upon  the 
actual  spindle  speed. 

The  highest  speeds  are  only  practicable  with  about  36^ 
to  40^  counts  under  normal  conditions. 

Productions  in  Ring  Spinning. 


Actual  speeds  of 

Produotiou  in 

Actual  speeds  of 

Production  in 

Count. 

spindles  per 

hanks  per  spindle 

Count. 

spindles  per 

hanks  per  spindle 

minute. 

per  55J  hours. 

minute. 

per  55i  hours. 

16 

7000-8000 

43-51 

40 

9500-11,000 

39-45 

20 

7500-8500 

43-48 

50 

8500-10,000 

31-37 

24 

8000-9000 

42-47 

60 

8500-10.000 

28-34 

28 

8.500-9500 

41-46 

70 

8000-9000 

25-5-30 

36 

9000-10,500 

39-45 

80 

8000-8500 

24-25-5 

Productions  in  Ring  Spinning. — In  spinning  yarns  from  single 
roving,  with  a  high  draft,  or  from  an  inferior  or  irregular  stapled 
or  soft  cotton,  or  in  exposed  buildings,  lower  speeds  are 
necessary. 

The  ring  spinning  machine  cannot  be  as  profitably  em- 
ployed in  the  production  of  yarns  other  than  the  best  descrip- 
tions, when  in  competition  with  those  produced  in  the  mule 
spinning  machine. 

Ring  frames  require  better  cotton  and  finer  roving  for  the 
ordinary  classes  of  yarn.  They  are  principally  employed,  in 
this  country,  in  the  production  of  the  following  yarns  : — 

(1)  Yarns  containing  above  the  average  twist. 

(2)  Yarns  made  from  above  the  average  quality  of  cotton  for 
the  count. 

(3)  Yarns  of  above  the  average  quality. 

(4)  Yarns  which  are  required  in  bundle  or  warp  form  for  the 
subsequent  requirements. 

In  all  these,  this  machine  can  produce  to  greater  advantage 
when  the  counts  are  within  a  certain  range. 

'  Sec  effects  of  twists  in  single  yarns,  p.  215. 


2U  COTTON   SPINNING  CALCULATIONS 


Twist  Standards  for  Single  Yarns. 

The  object  in  applying  twist  in  spinning  yarn  is  to  secure  a 
common  bond  amongst  the  fibres,  and  thereby  create  a  certain 
tensile  resistance  to  tension.  The  purposes  for  which  the  yarn 
is  required  will  therefore  control  the  extent  of  the  twist  applied. 

The  ordinary  standards  in  use  are  as  follows  : — 

Mule  Yarns. — 

Turns  per  inch  in — 

V^count  X  3*18    =  Egyptian  weft 
Y^coun^  X  3'25    =  American  weft 
y/count  X  3'39    =  Egyptian  medium 
\/count  X  3*5      =  American  medium 
^count  X  3*606  =  Egyptian  twist 
^count  X  3"75    =  American  twist 
Ring  Yarns. — 

"  Soft  weft "  =  Vcount  X  3-25 
/       "  Medium  weft  "  =  A/count  X  3-5 
/  "  Soft  twist  "  =  v'^ount  x  3*75 


\/count  X  4*0      =  Ordinary  twist 

^count  X  4'2o     =  Water  twist 

^/count  X  4"5       =  Hard  twist 
\       ^couut  X  4*75    =  Extra  hard  twist 
\   v^count  X  5-5-9"0  =  Crepe 

The  above  twists  are  not  rigidly  adhered  to.  Slight  modi- 
fications are  made  in  them  by  the  spinner,  such  as  circumstances 
connected  with  the  operation  of  spinning  render  expedient. 

A  knowledge  of  the  effects  of  twist,  apart  from  the  ordinary 
standards,  is  most  essential  in  spinning. 

The  influence  wielded  by  twist  varies  with  the  character  of 
the  cotton.  It  is  greater  in  those  fibres  which  are  long,  uniform 
in  their  length,  and  silky  in  texture,  and  well  prepared.  The 
shade  of  the  yarn  is  always  darkened  with  increased  application, 
and  the  touch  is  also  hardened.  A  decided  curl,  or  shrink,  is 
also  thereby  developed.  This  latter  tendency  is  greatest  in  yarn 
which  is  irregular  in  diameter  or  made  from  harsh  cotton. 


AND   COSTS   OF    YARN 


215 


Yarns  that  are  highly  twisted  are  less  absorbent  and  colder 
to  the  touch,  more  difficult  to  dye  satisfactorily.  Such  often 
become  weaker  in  sizing,  bleaching,  and  dyeing,  whereas  those 
less  twisted  are  not  unusually  strengthened  thereby. 

The  Effects  of  Twist  in  Single  Yarn.— The  effect  of  twist 
upon  the  strength  of  yarn  is  graphically  illustrated  in 
Fig.  44.  This  diagram  was  prepared  from  the  breaking 
resistance  of  20'  yarn  made  from  Gd.  Brown  Egyptian  cotton. 
This,  in  its  preparation,  had  been  combed  and  otherwise  most 


1  -        2 


4  5  6 

TWIST    CONSTANTS 

Fig.  44. 


10 


carefully  prepared.  In  spinning,  double  roving  was  used.  These 
abnormal  conditions  being  considered  essential  for  the  end  in 
view,  as  it  must  be  recognized  that  to  obtain  the  most  satisfactory 
results,  such  work  could  only  be  useful  by  attaining  the  best 
conditions.  Yarns  were  prepared  containing  twist  ranging  from 
13  to  41-5  turns  per  inch.  In  testing  their  strength  the  greatest 
care  was  exercised  to  ensure  reliable  results.  Altogether  the 
number  of  tests  made  exceeded  12,000. 

In  testing  the  yarns,  considerable  difficulty  was  experienced, 


216  COTTON   SPINNING  CALCULATIONS 

ill  using  the  ordinary  strength  testers,  with  those  hardest 
twisted,  and  the  results  obtained  were  unreliable. 

Ultimately,  the  tests  were  accomplished,  satisfactorily,  by 
using  the  Moscrop  patent  single  thread  tester  made  by  Messrs. 
Cook  of  Manchester.  The  whole  of  the  tests,  made  use  of  in 
plotting  this  diagram,  were  executed  on  the  same  machine. 

The  diagram  gives  the  strength  developed  in  terms  of 
an  increasing  twist  constant,  and  also  in  strength  per  turn  of 
twist.  The  upper  curve  shows  the  former,  and  indicates  the 
point  at  which  twist  ceases  to  add  to  the  strength,  and  the 
lower  curve  shows  that  obtaining  the  greatest  value  in  strength 
per  turn  of  twist  inserted. 

The  inferences  drawn  from  these  tests,  and  from  inspection 
/of  the  yarn,  are — 

(a)  That  in  the  best  yarns  the  strength  contributed  per  turn 
of  twist  becomes  gradually  less  at  \/count  X  3. 

(b)  That  in  the  best  yarns  the  strength  ceases  to  increase 
with  the  added  twist  at  \/count  x  5. 

(c)  That  the  shade  and  touch  and  tendency  to  shrink  becomes 
appreciably  affected  after  \/count  X  3*5. 

(d)  That  the  shade  is  only  very  slightly  affected  up  to 
3'0\/count,  and  after  5Y/count  it  becomes  very  appreciably 
darkened. 

(e)  A  coincidence  was  that  the  twist  constant  realizing  the 
greatest  strength  per  turn  of  twist  was  3'17\/ count.  That 
adopted  by  the  trade  generally  in  spinning  weft  from  Egyptian 
cotton  is  3'18\/count. 

Twist  Standards  for  Folded  Yarn. — The  following  are  the  twist 
constants  used  in  doubling  : — 
Twofolds— 

XXXX  Soft 1-34 

XXX    „ 1-52 

XX    ,, 1-8 

X    ,, 2-2 

O.Q 
}J ^  O 

Medium 3*39 

Common 4'0 


AND   COSTS   OF   YARN 


217 


Lisle .... 
Double  spun  . 
Hard      .     .     . 


X 
XX 


4-5 

5*0  (singles) 

5-0 

5-4 

5-6 


Single  yarn. 


Sewings  Constant  or  Co-efpicient. 


Twofold. 


Six-cord. 


As  low  as  possible  M^S^^^^^^  ^  constaut      ^ 

4-5 


single  constant 


6 


X  constant 


6-5 


Single  yarn. 


Weft  to  twist  turns 


Crochet. 


Twofold. 


6-5 


Yarns  for  Fish  Xettixg. 


•Single  yarn. 

Twofold. 

Common  .... 

/      single  count 
\/  number  of  singles 
X  4o 

Six-cord. 


single  count 
number  of  singles 
X  6-5 


Kkitting  Yarns  and  Embroidery  and  for  Mercerizing. 


Singles. 

Fold. 

As  low  as  practicable    .     . 

/          singles 
\/  number  of  singles 
X  30  to  3-25 

218 


COTTON   SPINNING   CALCULATIONS 


The  Influence  of  Direction  of  Twist  in  Folded  Yarn. 

The  diagram  (Fig.  45)  shows  the  influence  of  the  direction 
of  twist  upon  the  strength  in  the  twofold  yarn.  This  figure 
was  plotted  from  the  breaking  strains  of  two  series  of  twofold 
yarns,  one  set  being  twisted  reversely  and  the  other  twisted 
in  the  same  direction  as  that  contained  in  the  singles.     The 


3  4  5  6 

TWO-FCLD  TWIST  CONSTANTS 

Fig.  45. 


single  yarns  used  were  of  very  good  quality  and  ah  alike,  con- 
taining twist  to  the  extent  of  3"6\/count,  per  inch.  The  twofold 
twists,  per  inch,  ranged  from  2"5-\/count  to  6*85\/count.  Those  ] 
twisted  in  the  same  direction  as  the  single  were  harder  to  the 
touch  and  darker  in  shade,  and  with  the  increased  twist,  their 
elasticity,  to  tensile  resistance,  increased  to  an  abnormal  extent. 
Yarns  for  elastic  fabrics  and  in  preparing  for  sewing  threads 
have  their  twist  in  this  direction.  Those  twisted  in  the  reverse 
direction  exhibited  no  abnormal  features ;  a  slightly  darkening 
shade  was  noticeable  especially  in  those  fullest  twisted. 

The  Influence  of  Varying  Degrees  of  Single  and  Folding  Twist. — 
Fig.  4G  was  prepared  from  the  breaking  strains  of  yarns  con- 
taining a  graduated  extent  of  twofold  twist,  and  made  from 


AND   COSTS   OF   YARN 


219 


single  yarn  containing  the  following  twists  per  inch  :  (1)  2"9, 
(2)  3-35,  (3)  3-9,  and  (4)  4-5  times  the  y'counts.  The  doubling 
twist  was  inserted  in  the  reverse  direction  to  that  in  the  singles, 
and  the  twofolds  comprised  20  differently  twisted  threads, 
ranging  in  extent  from  v^counts  X  2"75  to  ^/counts  X  5-95. 

The  following  were  the  most  noticeable  differences  in  features 
of  these  yarns  : — 

Number  (4)  gave  the  best  strength  when  containing  doubling 
twist  to  the  extent  of  5y/count  and  below.  It  was  small  and 
pearly. 

Number  (1)  was  the  most  attractive  yarn,  being  softest,  most 


35 


TWIST  PER  INCH 

9   10   11   12   13  14   15   16   17   18  19   20 


1 

^^ 

_     - 

s.^1        . 

^ 

f^ 

2^ 

^ 

^ 

^ 

^^ 

X^d 

r 

\ 

4' 

r^ 

y^ 

/ 

\ 

_^ 

^ 

/ 

V 

3* 

' 

^ 

> 

V 

^^ 

^* 

< 

\ 

2- 

-^ 

X^ 

~1- 

r*«-i 

_  25  —^-^ — 


3  4  5  6 

TWO-FOLD  TWIST  CONSTANTS 

Fig.  46. 


cylindrical,  and  lustrous.  In  point  of  strength,  however,  it  is 
inferior  to  the  others,  up  to  4-9v/counts,  turns  per  inch,  but  a 
little  beyond  this  point  its  strength  is  superior  to  the  others.  Of 
the  four  types  this  would  be  the  most  expensive  yarn  to  produce. 

This  figure  is  useful  in  indicating  the  twofold  twist  most 
beneficial  in  variously  twisted  single  yarns;  also  the  most 
serviceable  single  twist  when  a  given  twist  is  desired  in  the 
twofold. 

The  Effects  of  Twisting  Two  or  More  Single  Threads  together. — 
When  the  twist  inserted  is  in  the  reverse  direction  to  that  con- 
tained in  the  singles,  it  displaces  an  equal  amount  from  each 
of  them.     When  the  twisting  proceeds  in  the  same  direction  as 


220  COTTON   SPINNING   CALCULATIONS 

that  contained  in  the  singles,  that  in  the  singles  is  supplemented 
to  the  extent  of  the  doubling  twist.  Thus,  the  former  procedure 
removes  the  twist  in  the  singles,  the  fibres  being  simply  re- 
arranged convolutely,  or  in  what  may  be  termed  a  spiro-corrugate 
order.  When  tension  is  applied  to  bodies  of  fibres  so  arranged 
they  are  pressed  towards  a  common  centre,  and  this  force  bonds 
them,  preventing  the  fibres  from  sliding. 

It  is  this  change  in  the  arrangement  of  the  fibres,  without 
necessarily  changing  their  compactness,  that  is  responsible  for 
the  greatly  increased  strength  of  doubled  yarn  as  compared 
with  that  of  single  yarn  of  a  similar  weight. 

The  conditions  that  would  have  to  obtain  in  order  to  utilize 
to  the  fullest  extent  the  available  strength  of  the  body  of  fibres 
contained  in  a  doubled  yarn,  are — 

That  all  fibres  be  equally  outstretched  and  in  alignment,  so 
that  they  mutually  share  the  tension  applied.  That  they  are 
bonded  sufficiently  to  prevent  their  slippage  upon  each  other 
and  devoid  of  individual  twist. 

This  latter  state,  in  so  far  as  twist  is  concerned,  can  readily 
be  obtained.  It  is  in  the  laying  of  the  fibres  equally  outstretched 
that  difficulty  arises,  that  state  being  only  partially  possible. 
The  formation  of  the  fibres  about  a  common  centre,  twisted, 
renders  their  alignment  impossible. 

The  aims  of  doubling  may  be  stated  as  follows  : — 

(1)  To  permanently  utilize  the  available  strength  of  the 
fibres  by  preventing  their  axial  movement  after  the  thread  is 
completed. 

(2)  To  obtain  the  desired  compactness,  lustre,  and  freedom 
from  ooze,  with  the  fibres  bonded  in  the  most  suitable  manner 
for  the  required  size  of  thread. 

(3)  To  insure  definite  elastic  properties  in  the  yarn  when 
under  tension. 

(4)  To  obtain  the  desired  character  of  surface,  such  as 
cylindrical,  spiral,  corkscrew,  pearly,  crepe,  or  other  effects. 

In  order  to  secure  the  utmost  strength,  and  at  the  same  time 
prevent  axial  movement,  the  twists  in  the  successive  stages 
should  be  arranged  so  that  they  balance  in  the  completed 
yarn. 


AND   COSTS   OF   YARN  221 

Compactness  is  the  result  of  tension  and  compression  applied 
during  doubling.  In  order  to  obtain  the  smallest  thread  from 
a  number  of  others,  as,  for  example,  in  sewings  and  kindred 
3'arns,  the  following  procedure  is  most  effective  : — 

In  doubling  the  singles  the  fibres  should  be  compressed  to 
their  limit,  by  twisting  in  the  same  direction  as  the  singles,  and 
to  the  extent  necessary  to  obtain  a  balanced  state  when  the  final 
twisting  is  completed.  Thus,  when  the  final  twist  is  great,  that 
in  the  folded  singles  must  also  correspond.  In  the  substitution 
of  the  preparing  by  the  final  twist  the  consequent  extending 
and  expanding  tendencies  are  fully  absorbed,  or  counteracted 
by  their  greater  radius  about  a  common  centre. 

Lustre  is  affected  by  the  angle  which  the  fibres  make 
with  the  completed  thread.  It  is  greatest  when  they  are  in 
line  with  the  axis  of  the  individual  singles,  and  vice  versa. 
Thus,  lustre  indicates  the  extent  of  the  twist  in  the  singles 
and  in  the  fibres. 

Freedom  from  Ooze. — This  is  in  the  main  the  result  of  the 
rolling  action  of  the  yarns  against  each  other  in  the  course  of 
twisting. 

The  Tendency  to  Stretch,  under  tension,  is  regulated  by  the 
angle  of  the  singles  or  strands  comprised  in  the  final  thread. 
The  more  numerous  these  are  the  less  their  stretching  tendency. 
Thus,  highly  elastic  doubled  yarns  are  composed  of  the  fewest 
singles  and  strands.  The  number  of  strands  that  can  be  satis- 
factorily bound  in  this  way  are  limited,  and  hence  they  seldom 
exceed  four.  Above  this  number  the  singles  or  strands  have 
insufficient  adherence,  and  hence  plaiting  is  resorted  to. 

Cylindricity  is  developed  most  effectively  when  the  singles 
are  only  slightly  twisted  and  of  the  best  quality. 

Pearly  Effects  are  developed  by  employing  highly  twisted 
singles. 

Crepe  by  twisting  in  the  same  direction  as  the  singles, 
also  by  inserting  considerable  twist  in  the  reverse  direction  to 
that  in  the  singles ;  but  the  effect  is  not  the  same  in  both  cases. 

Spiral  Effects  are  obtained  by  slight  folding  twist. 

Where  a  small  yarn  with  hard  effects  are  required,  highly 
twisted  singles  are  necessary.     For  soft  effects  similar  to  those 


222  COTTON   SPINNING  CALCULATIONS 

required  in  yarns  for  mercerizing,  the  singles   should  be  softly 
twisted. 

Corkscrew  Effects  are  obtained  by  doubling — 

(a)  Yarns  in  unequal  tension. 

(h)  Yarns  unequal  in  size. 

(c)  Yarns  containing  unequal  twist. 

(d)  Yarns  twisted  in  opposite  direction. 

The  Relative  Resistance  of  Yarns  to  Twist. — Assuming  the 
CO- efficient  of  resistance  to  the  first  twist  in  a  given  length  of 
yarn  to  be  1,  and  the  resistance,  as  the  twist  progresses,  directly 
proportional  to  the  twist  contained,  the  relative  resistance,  when 
the  diameters  of  the  yarns  are  not  alike,  being  proportionate  to 
their  diameters  cubed— then,  upon  these  assumptions,  the 
relative  resistance  of  a  body  of  untwisted  fibres,  equal  to  60^* 
and  40*  yarns,  are  respectively — 

When  the  fibres  are  twisted,  their  resistance,  when  t  denotes 
the  twist  contained  in  them,  will  be  respectively — 

.(iYand^(4=f 
V\/60/  \v'40/ 

The  above  are  based  on  other  conditions  being  equal. 
The  relative  resistance  of  60'  and  40^  yarns  containing  twist 
to  the  extent  of  3*5>/count,  is  therefore  expressed  as  follows : — 

60%  3-5v/6o(-^y=-057 

40%  3-5v/40(-^y=-0837 

When  folded  threads  are  required  balanced,  namely,  without 
tendency  to  twist  or  untwist,  it  is  necessary  to  insert  twist  to  the 
extent  that  will  balance  the  forces  they  contain.  Thus,  a  yarn 
composed  of  several  single  threads  should  be  twisted  so  that  the 
force  developed  by  the  doubhng  twist  is  sufficient  to  counteract 
those  still  contained  in  the  singles.     When  a  number  of  singles 


AXD   COSTS   OF   YAEX  223 

are  bound  by  twist  in  tbis  manner,  the  twist  inserted  adds  to,  or 
reduces,  that  in  each  single,  to  a  corresponding  extent.  This 
action  reduces  or  increases  the  force  which  the  singles  exert. 
Therefore,  when  the  doubling  twist  is  inserted  in  the  reverse 
direction  to  that  in  the  singles,  and  to  the  extent  of  rendering 
the  opposing  forces  equal,  the  yarn  is  then  in  a  state  of  equili- 
brium or  "  still."  The  amount  of  twist,  which  is  required  to 
produce  the  still  or  balanced  state,  will  be  governed  by  that  con- 
tained in  the  singles  and  also  by  the  number  of  threads 
comprised  in  folding.  Hence,  the  more  numerous  the  twists  in 
the  single  and  the  fewer  the  folds,  the  greater  the  amount  of 
twist  required  in  doubling  the  yarn. 

The  extent  of  the  twist  required  in  folding  yarns  to  balance 
that  in  the  single  yarn  may  therefore  be  ascertained  in  the 
following  manner : — 

Let  ci  =  the  count  of  the  single. 

0-2=  ,,         ,,         folded  yarn. 

Ti  =  the  twist  in  the  single  yarn. 
T2  =         ,,        required  in  the  folded  yarn. 

The  relative  twist  required  to  develop  a  balance  of  the  forces 
in  the  completed  thread,  when  twofold,  is  as  follows  ; — 
The  force  in  the  singles  before  folding  is  : 


'Hvm 


The  force  due  to  the  twist  remaining  in  the  singles  when 
doubling  is  completed  is  : 


'b'^  -  <37)1 


The  force  due  to  the  doubling  twist  in  the  thread  is 
Therefore,  the  forces  in  a  balanced  thread  are : 


224  COTTON   SPINNING   CALCULATIONS 

The  above  formula,  when  applied  to  twofold  50*  with 
ti  =  3"5\/ci,  gives  the  following  results  : — 

t.2  =  10-9 

This  method  of  ascertaining  the  twist  is  applicable  to  all 
kinds  of  yarns.  It  enables  that  necessary,  in  the  singles,  to 
balance  a  certain  folding  twist  to  be  ascertained,  or  vice  versa. 
Adherence  to  this  method  would  necessitate  considerably  more 
twist,  in  the  single  yarn,  than  it  is  customary  to  apply,  and 
hence  it  would  increase  the  cost  and  this  without  commensurate 
return.     In  certain  classes  of  yarns  it  is  applied  to  some  extent. 

The  application  of  the  above  formula  is  further  illustrated  by 
the  following  example  : — 

Let  the  count  of  the  single  be  50,  and  twofold  is  made  containing  the  usual 
turns  ^^2  X  4  =  20.  "What  twist  would  be  necessaiy  in  the  singles  in  order  that 
the  completed  twofold  be  in  perfect  balance  ? 


.•.[(x,/60-20)(-.y>  =  -^ 


_  , 20 

V50y  J         V25 

a;V50  =  46-5 

X  =  6*58,  the  single  twist  coefficient 

or  constant 


The  Eixg  Doubling  Fra^te. 

Fig.  47  represents  the  gearing  common  in  ring  doubling 
frames,  A,  Ai  being  the  rollers,  and  L  the  driving  pulleys,  J  the 
tin  roller,  and  I  the  tin  roller  shaft  wheel,  the  train  I,  H,  G, 
E,  El,  D,  Di,  Ci,  B,  and  Bi,  being  the  trains  of  wheels  con- 
necting the  front  rollers  to  the  tin  roller.  K  and  K  are  the 
spindles. 

The  following  twist  is  obtained  when  the  smallest  sizes 
of  the  change  wheels  are  employed  : — 

The  revolutions  of  the  spindle  per  one  of  the  roller,  with  the 
smallest  sizes  of  change  wheels,  are — 


AND   COSTS   OF   YARN 


225 


75  X  60  X  120  X  8 
20  X  20  X   20  X  IJ 


=  480 


and  therefore  the  twist  per  inch  inserted  in  the  yarn,  on  the  left 
side  of  this  machine,  would  be — 

lii  V  22  =  87-27 

whilst  that  on  the  right  side  would  be — 

480 
21  X  -^^  ~  ^^ 

The  range  of  twist  with  20-60  the  available  sizes  of  top 


Fig.  47. 

change  wheels,  when  the  tin  roller  and  the  lower  twist  wheels 
are  both  20,  is — 

On  the  left  side,  from  87-27,  to  87-27  X  §!]  =  29-09  ■ 
On  the  right  side,  from  61,  to  61  x  fB  =  20-3 

With  the  available  sizes  of  wheels  for  G,  when  the  tin  roller 
wheel  is  20  and  C  is  60,  the  twist  per  inch  procurable,  ranges 
from 

On  the  left  side,  from  29-09,  to  ^^'^^  ^  ^^ 


On  the  right  side,  from  20-3,  to 


60 

20-3  X  20 
60 


=  9-69 
=  6-77 


226  COTTON   SPINNING   CALCULATIONS 

With  the  tin  roller  40  and  the  other  change  wheels  60  and  60, 
the  twist  would  be — 

On  the  left  side, ^n =  4*89  twist  per  inch 

On  the  right  side, j^ =  3-38  twist  per  inch 

r„,  ,     ,.  ..     »  ,.  revolutions  of  spindle  (actual) 

The  production  per  unit  of  time  = -1—^-, —     ■ — r^ ' 

^  twist  required 

=  inches  per  unit  of  time 

Therefore  with   the  spindles  making   8000  revolutions  per 

minute  (actual),  and  the  counts  2-72*  and  twist  coefficient  1'5, 

the  rate  of  production  in  hanks  and   ounces   per  spindle  per 
10  hours,  no  allowances,  would  be — 

8000  X  60  X  10  =  revolutions  of  spindle  per  10  hrs. 

8000  X  60  X  10       .     ,  •   ;n    •     1A  1 
=^^ =  inches  per  spmdle  in  10  hrs. 

8000  X  60"x  10  ,  •   ;ii    •     iA  I 
= =  yards  per  spindle  m  10  hrs. 

4-5  vZ-'g-  X  36        -" 
8000_x  60  x  10      ^  j^^^j^g      ,  ^  .^^^^  .^  jQ  j^^.g^ 
4-5  ^/l^-  X  36  X  840 
8000x60x10x16     ^  ^^^^^^  .^^1^  .^^  10  1^^.^ 

4-5  V^X  36  X  840  X  ^2_ 
This  is  assuming  the  yarn  does  not  contract. 

=  revolutions    of    the    roller    per 


4-5  \/^2-  X  If  X  ^  minute  on  the  left  side 

=  revolutions    of    the    roller    per 


4-5  x/^2.  X  2i  X  -2^  minute  on  the  right  side 

"With  the  particulars  of  the  frame  as  given  in  the  figure,  the 
different  top  change  wheels  that  would  be  applicable,  in  order 
that  the  same  turns  may  be  put  in  the  yarn  made  on  both  sides 
of  the  machine,  are  as  follows :  The  ratio  of  these  change 
wheels,  left  to  right,  should  be  as  ^  :  1^,  or  10 :  7,  or  1 :  0  7. 

The  following  exercises  are  based  on  the  conditions  obtaining 
in  Fig.  47 :— 


AND   COSTS    OF    YAKN  227 

Exercises  1.  What  size  of  wheel  Bj  would  give  twist  identical  to  that  on  the 
left  side  with  top  change  wheels  20  ? 

2.  Assuming  B,  and  B  107  and  75,  respectively,  with  the  top  change  wheels 
C,  Cj  alike  and  G,  60,  whilst  the  yarn  doubled  is  2-60' ;  what  sizes  of  G  would  be 
suitable  for  iising  2-70',  2-80%  2-90",  the  same  twist  coefiScient  in  each  instance  ? 

3.  Assuming  the  tin  roller  wheel  20  and  bottom  change  wheel  G  20,  what 
size  of  C  and  G^  would  be  necessary  for  2-120'  on  both  sides,  the  twist  constant 
being  4'5  ? 

4.  Assuming  that  2-120',  containing  35  turns  per  inch,  is  being  doubled  on 
both  sides,  at  what  rates  per  minute  should  the  rollers  rotate  ? 

5.  What  twist  per  inch  would  be  inserted  when  the  2^ -inch  roller  is  observed 
to  make  1  revolution  per  70  of  the  spindle  ? 

6.  If  the  twist  is  8-0  turns  per  inch  with  a  60  lower  change  wheel,  what  size 
of  wheel  will  give  2-4  turns?  Also,  at  what  rate  must  the  roller  rotate  per 
minute  in  both  instances,  assuming  the  spindle  makes  600  revolutions  per  minute  ? 

7.  The  top  and  bottom  change  wheels  are  60  and  40  respectively,  and  the 
present  twist  is  24-8  turns,  but  25-8  are  required  :  which  change  wheel  would  alter 
to  get  the  nearest  to  this,  and  what  size  of  wheel  would  be  necessary  ? 

8.  If  the  twist  per  inch  was  24*8  and  the  top  and  bottom  change  wheels,  60 
and  40  respectively,  are  each  changed  for  wheels  three  teeth  less,  what  would  be 
the  alteration  in  the  twist  ? 

9.  Give  several  sets  of  top  and  bottom  change  wheels  which  would  give 
identical  twists  to  those  obtained  with :  20  top  and  60  bottom,  21  top  and  56 
bottom. 

Changes  in  the  sizes  of  the  tin  roller  shaft  and  bottom 
change  wheels,  affect  both  sides  equally. 

Alterations  in  the  twist  by  means  of  the  top  change  wheels 
must  be  made,  on  both  sides,  inversely  to  the  changes  in  the 
twist  required. 

The  rate  of  the  production  is  altered,  by  changes  in  any  of 
those  wheels,  in  the  direct  proportion  to  the  alteration.  When 
changing  counts  of  yarns,  and  the  twist,  required,  involves  the 
same  twist  coefficient,  then  the  sizes  of  the  wheels  required  are 
inversely  as  the  v'counts.  Thus,  if  changing  from  2-30'  to 
2-40%  present  wheel  :  required  wheel  : :  v^intended  count  : 
V^present  count. 

When  the  wheels  required  for  carrying  out  the  change  desired 
at  one  or  two  of  these  points  are  not  available,  the  results 
desired  may  be  obtained  by  changing  at  the  other  points  in  the 
same  proportion. 

The  speed  of   the    spindles   applicable   for  various  counts 


228 


COTTON   SPINNING  CALCULATIONS 


range  from  3000  to  8500,  according  to  the  class  of  work.  When 
changing,  ahvaj^s  consider  whether  the  new  circumstances  will 
admit  of  or  require  a  change  in  the  speed  of  the  spindles.  Such 
is  made  by  altering  the  frame  shaft  pulleys  or  their  drivers, 
whichever  be  most  convenient. 

Slippage  in  Doubling  Frames. — In  doubling  frames  there  is 
usually  considerable  slippage  in  driving  the  spindles  from  the 
tin  roller,  and  this  often  results  in  undesirable  variations  in  the 
twist  which  the  yarn  contains.  An  idea  of  the  extent  of  this  is 
contained  in  the  following  observed  speeds  in  a  ring  doubling 
frame  in  good  working  condition.  This  frame  contained  one 
tin  roller  making  838  revolutions  per  minute  and  8  inches  in 
diameter,  the  spindle  wharves  being  1^  inch  in  diameter.  The 
following  were  typical  records  of  their  speeds  per  minute  :  5186, 
5100,  5416,  5265,  their  calculated  rate  being  5950,  and  hence 
the  loss  was  12*8,  14"3,  9"0,  11*5  per  cent,  respectively.  This 
is  when  neglecting  the  size  of  the  spindle  band.  It  will  be 
noticed  that  when  the  size  of  the  spindle  band  is  allowed  for 
in  this  instance,  the  loss  will  be  almost  «?7. 

The  Twiner  Mule. — Fig.  48  contains  particulars  of  the  gear  for 
driving  the  spindles  and  drawing-out  scroll  shaft  in  a  twiner. 


Fig.  48. 


N,  N  are  the  strap  driving  the  rim  pulley  M ;  L  is  the  rim  pulley, 
and  LK  the  rim  band  driving  the  tin  roller  pulley  J,  K  being  the 
rim  band  carrier  pulley.  The  tin  roller  B  drives  the  spindle 
wharve  A ;  C  and  Ci  are  the  tin  roller  wheels,  shown  in  two 
sizes,  for  driving  the  train  D,  E,  F,  G,  H  ;  H  is  the  drawing-out 
shaft  clutch  wheel.     The  other  particulars  of  the  above  gear  are 


AND   COSTS   OF   YARN  229 

as  follows  :— Revolutions  per  minute  of  run  shaft,  770.  Rim 
L,  12-24  inches  ;  B,  6  inches  ;  J,  11  inches  ;  A,  i  inch  diameters 
respectively.  C  and  Ci,  15  and  25;  D,  80;  E,  20-40;  F,  90; 
G,  15;  H,  68,  teeth  respectively.  H  makes  3;]^  revolutions 
per  draw  in  moving  the  creel  out  72  inches.  The  twist  change 
wheels  are :  the  tin  roller  15  and  25,  and  the  wheel  E  20  to  40. 

The  rim  pulley  is  seen,  on  inspection  of  this  gear,  to  be  the 
medium  for  adjusting  the  speed  of  all  the  productive  parts,  and 
the  twist  change  wheels  for  altering  the  rate  at  which  the  yarn 
IS  introduced  to  the  twisting  influence. 

If  the  examples  relating  to  the  spinning  mule  have  been 
understood,  the  following  calculations  will  be  understood. 

Hence  only  one  example  is  given  in  each  set  of  these 
calculations. 

ExEKCiSE  1  -Calculate  the  revolutions  of  the  spindles  per  minute  with  con- 
secutive sizes  of  riras  ranging  from  12  to  24  inches  in  diameter. 

diaiSter'''~'^'''°^"^'°"'  ^'''  """'"^^  °^  'P'^^  ''''"'  ^^'^  ''"^  '^  ^-  '"<^^^«^  "^ 

11  X  i 

Size  of  rim      .    12"  13"  U"  15"  16"  17"  18"  19"  20"  21"    02"    93"    oi" 
Revs.ofspindle|5760        6720        7680        8640        9600        10,560  "^     11^520 
permmute    /        6240        7200        8160        9120       10,080        11,040 

chan^rSstTStst^^  '''  '^'''  '''  ''''-'  '-'^^  '''  ^'^'-S-^  ''-^^-  ^^-^ 
^^Emmj^Ic-Beyolntions  of  spindle  per  one  draw  and   per  3f|  revolutions 

3iix  68  X  90x  80x  6      ,    . 

lE~x~W^<r25x^^  ~  l-*^^  "^'^'^^  °^  ''-  inches 

.-.  the  twist  per  inch  =  ^58  x  68  x  90  x  80  x  6  x  8  _ 

68  X  15  X  40  X  25  X  72  X  7  ~    ^ 
When  the  tin  roller  wheel  is  ^ 
25  and  the  twist  change  is/    ^^      ^^      ^^      37      36      35      34      33      32 

The  twist  per  inch  is  /  ^'^'^  12-7  1.3-4  14-3 

I  11-8     124     13-05     13-8      147 


31  30  29  28  27  26  25  24  23   22   21   ^o 
15-7    16-8    18-1    19-6     21-4      03- x 
15-2    16-2    17-4    18-8    20-5     22-4 


{ 

Exercise  3.-Calculate  the  twist  change  wheel  that  will  give  the  nearest  to 
23  5  turns  per  mch  when  the  tin  roller  wheel  is  15. 


230  COTTON   SPINNING  CALCULATIONS 

ExEKCisE  4. — Calculate  the  twist  per  inch  with  consecutive  sizes  of  twist 
change  wheels  ranging  from  20  upwards,  with  the  tin  roller  wheel  15. 

Alls.  Twist  change  wheel  .     .  20      21       22      23  ...  30 

n,    •  ,        -1  /  37-5  34-2 

Twist  per  inch.     .     .    (3^.^  3^.3  ^6  3 

,     258  X  68  X  90  X  80  X  6  X  1      ^^  , 

Jiixamine.   jr^ ^-= ^77. ^-^ ^-5 -_  =  39*4 

^        68   X  15  X  20  X  15  X  72  X  I 

Exercise  5. — If  the  twist  change  wheel  35  and  the  counts  doubled  4,"',  what 
sizes  of  wheels  would  be  required  for  4f-',  -"o"-',  ^',  -^"-%  1^^',  when  the  same  twist 
constant  is  used  ? 

35  V^^- 
Example.  — -=^  =  wheel  suitable  for  ^\!^' 

ExERCiSE  6, — Estimate  the  production  in  hanks  per  spindle  and  in  pounds 
per  twiner  of  1000  spindles  per  10  hours ;  the  spindles  to  develop  a  speed  of 
11,000  revolutions  per  minute,  and  baching  off  and  winding  to  occupy  5  seconds  ; 
the  counts  doubled  are  ^Q-',  -"f-',  5^',  ^%  "#',  i^^-^%  and  the  twist  constant  4-5  is 
used.  Allow  15  per  cent,  for  loss  of  speed  during  twisting,  and  15  minutes  per 
doff,  the  cops  weighing  2  ozs.  each. 

Example.  — 4f-'. 

/4-5a/-^*x72\      100 
Seconds  taken  twisting  per  draw  =  I — ti-aaa /^O  -of-  =  10-04  seconds 

Seconds  per  complete  draw  =  10-04  +  5  =  15-04 

Time  to  make  a  cop  in  seconds  =  — "^^ ^^^ =  15-04  seconds 

^  72  X  85 

The  above  numerators  =  contents  of  a  cop  in  inches 

Time  taken  to  make  a  cop  and)  _  1  x  25  x  840  x  36  x  15-04      15 

doff  in  hours  /  ~  8  x  72  x   60  x  60  60 

=  5  hrs.  29  mins.  +  ~  hrs.  =  5-733  hrs. 
bO 

10    X   2   X  25 

.'.  production  in  hanks  per  spindle  =  K:noo tc. f  =  ^'45 

.".  i>roduction  in  pounds  per  twiner  =   ^.-^ =218  lbs. 

Changing  the  size  of  the  rim  affects  the  speed  of  all  the 
parts  concerned  in  twisting  and  introducing  the  yarn,  and  there- 
fore alters  the  time  occupied,  in  making  this  movement,  in  direct 
proportion ;  the  time  taken  to  back  off  and  wind  remaining 
unaffected. 

Changing  the  twist  change  wheel  alters  the  twist  through 
affecting  the  rate  of  movement  of  the  carriage,  in  the  direct 
proportion  to  the  change  made  in  the  wheel.     This  alters  the 


AND   COSTS   OF   YAPyN  231 

rate  of  the  carriage  movement  inversely  to  the  twist,  the  pro- 
ductive rate  being  affected  in  the  proportion  which  this  altera- 
tion affects  the  period  of  twisting. 

ExAMPLK.— Assuming  a  draw  is  made  in  15-04  seconds,  when  the  twist 
change  wheel  is  35,  and  of  this  5-0  seconds  is  the  time  occupied  in  backing 
off  and  winding ;  the  following  alteration  would  arise  in  the  event  of  employing  a 
23  twist  change  wheel : — 

10-04  X  35       .       . 

20 ~  ^^^^  ^^^  seconds  occupied  in  twisting 

/.  time  per  draw  =  17-57  +  5  -  22-57 

The  rate  of  production  is  therefore  altered  in  the  terms  of 
15'04  :  22-57  =  0'666,  and  not  in  proportion  to  the  change  in 
the  wheels,  0-657. 

Costs  of  Yarn. 

The  following  are  given  as  representing  about  the  average 
costs  of  the  various  items  of  expenditure  in  South-East 
Lancashire  mills  in  the  production  of  mule  yarns  of  medium 
count  from  uncombed  cotton  when  spun  from  single  roving  : 

Cost  in  pence  per 
spindle  per  annum. 

Banding — Twine — Rope        0-5 

Carriage  on  cotton  and  other  materials 2*3 

Coal 3-75 

Taper 0-15 

Cleaning  cloths — Engine  packing — Brushes 0*25 

Leather  and  cloth  for  rollers 0-5 

Belting  and  its  accessories 0-25 

Lubricants 0'9 

Repairs  :    Mill  buildings — Machinery  and  upkeep  :    basis ) 

1|  per  cent,  at  24s.  per  spindle  per  annum  j' 

Gas  and  water l-O 

Rates  and  taxes 2-0 

Stationery  —  Telephone  —  Exchange  —  Railway  tickets — ■! 

Stamps — Printing  and  sundry  office  expenses  J 

Sundry  stores 0-5 

Insurance 0-45 

Interest  at  5  per  cent,  at  25s.  per  spindle 15-0 

Depreciation  at  4  per  cent,  on  24s.  per  spindle      ....  11-52 

Wages 360 

80-64 

Percentage  of  wages  to  other  expenses     ...     45 


232  COTTON   SPINNING  CALCULATIONS 

In  order  to  ascertain  the  cost  of  producing  yarn  wben  the 
production  and  the  inclusive  expenses  per  spindle  are  known, 
the  following  is  the  course  usually  followed  : — 

To  the  cost  of  the  cotton  at  the  card  delivery  add  the  cost 
of  production,  per  pound,  and  deduct  the  sum  received,  per 
pound  of  yarn  spun,  for  the  waste. 

The  rate  of  the  production  per  spindle  in  the  South-East 
Lancashire  district  does  not  vary  considerably.  The  range  is 
given  on  p.  204. 

In  costing  it  is  usual  to  disregard  the  loss  arising  from 
waste  after  the  card,  because  this  item  is  about  balanced  by  the 
regain  in  conditioning.  The  value  of  the  waste  is  assessed  at 
2^  per  cent,  of  the  cotton  price  ;  this  is  considered  a  fair  value. 

Example  of  the  cost  of  28"  T.  made  from  Middling  American  cotton  at  6d. 
per  pound. 

Cost  in  pence 
per  pound. 
Working  costs  per  spindle  per  annum SOGi  \ 

Production  per  spindle  per  annum,  based   on  50  „.;,       k^  [     =  1-413 
working  weeks  per  year  and  32  hanks  per  week    "   „ — 

Cost  of  the  cotton  delivered  at  the  card  delivery, 

allowing  10  per  cent,  for  loss,  ^       —  "'"' 

8-083 

Less  value  of  the  waste 0-15 

,,     cost  of  raw  cotton 6-0 

6-15 

Nett  cost  of  spinning 1  -933 

Add  :  cost  of  selling  and  discounts  3i  per  cent  on  selling  price. 

Example  36'  T.  from  F.  Middling  American  cotton  at  Q-Wd.  Production, 
30  hanks  per  spindle  per  week. 

Cost  in  pence 
per  pound. 

Working  costs  per  spindle  per  annum,  80-64  ^  _  80*64  x  36  _  -i.qok 

Production  per  spindle  per  annum,  50  x  30  hanks  /         30  x  bO 
Cost  of  the  cotton  at  the  card  delivery,  allowing 

10  per  cent,  loss 6*844 

8*779 

Less  value  of  the  waste 0*154 

„    cost  of  the  cotton 6*16 

6-314 

Nett  cost  of  spinning 2-465 


AND   COSTS   OF   YARN 


233 


Example  60'  T.  Fair  Br.  Egyptian  at  dd.  per  pound. 

Working  costs  per  spindle  per  annum 80'64 

Production  per  spindle  per  annum |^  X  50 

Cost  of  the  cotton  delivered  at  the  card  10  per 

cent,  wasted,  ' — ^t, — 


Cost  in  pence 
per  pound. 

=  4-032 


10-0 


14-032 

Less  value  of  the  waste 0*225 

,,    cost  of  cotton 00 

9-225 

Nett  cost  of  spinning 4  807 

The  Approximate  Costs  of  Yars  when  Spun  from  Single  Koving,  the  Basis 
BEING  8064  Pemce  Cost  per  Spindle  per  Annum  =  161  Pence  per  Spindle 
PER  Week. 


t- 

a> 

<»  1 

a> 

<D 

^ 

^tn 

1 

°.S 

fcoS 
CO 

"(G 

a 

a° 

II 

la 

=3    OJ 

P.5 

"-I. 

Count  and 

description 

of  yarn. 

at 

.2  c 
II 

■3-0 
2  & 

Suitable  cotton  and 
grade. 

Price  of  cotton  at  t 
of  compilatio 

=1  ■ 

?^  S  " 

If 

"  3 

a-a 
l§ 

*"  is 
Jl 

II 

•a  s 

P 

1  ° 
to  o 

■£  s 
o  o 

Prime  cost  of  yarn  i 
per  pound. 

Margin     between 

cost  of  yarn  and 

the  raw  cotto 

1 

^  G.O.  American! 

16  W. 

34 

,  /G.  Broach       > 
2\G.Tinnevelly) 

5-55 

12 

6-31 

0137 

0-76 

6-933 

1-383 

16  T. 

34 

G.O.  American 

5-71 

12 

648 

0-142 

0-76 

7-098 

1-388 

16  T.  super. 

33 

s.L.M.      „ 

5-95 

11 

6-68 

0149 

0-783 

7-314 

1-364 

20  T. 

34 

b. 

5-86 

11 

6o8 

0147 

0-95 

7-383 

1-523 

20  W. 

34 

G.O. 

5-71 

12 

648 

0142 

0-95 

7-288 

1-578 

24  T. 

34 

s.L.M.       ,. 

5-95 

11 

6-68 

0149 

1-14 

7-671 

1-721 

24  W. 

34 

f.G.O. 

5-81 

12 

66 

0145 

114 

7-595 

1-785 

SOT. 

32 

b.M. 

605 

11 

6-8 

0-151 

115 

7-799 

1-749 

30  W. 

32 

s.L.M.      „ 

5-95 

11 

6-68 

0-149 

115 

7-681 

1-731 

32  T. 

30 

M. 

609 

10 

6-77 

0-152 

1-72 

8-338 

2-329 

36  T. 

29 

f.M. 

6-2 

10 

6-9 

0-155 

2-0 

8-745 

2-545 

36  W. 

31 

b. 

605 

11 

6-8 

0151 

1-88 

8-529 

2-524 

40  T. 

28-5 

G. 

6-31 

10 

70 

0-158 

2-20 

9-102 

2-792 

42  W. 

28-5 

8.                      „ 

615 

10 

6-83 

0154 

2-38 

9-056 

2-906 

50  T. 

26 

M.F. 

6-55 

10 

7-28 

0164 

3-1 

10-216 

3-666 

50  W. 

26 

G.M. 

6-31 

10 

7-0 

0-158 

31 

9-943 

3-633 

GOT. 

23 

j  Special  select 
I    grades  only 

60  W. 

24 

M.F.  American 

6-55 

10 

7-28 

0-164 

403 

11-146 

4-596 

In  those  spinning  mills  preparing  the  yarn  from  double  roving, 
at  the  spinning  machine,  the  cost  of  the  working  expenses  are 


234 


COTTON   SPINNING   CALCULATIONS 


greater  than  those  previously  given.    This  has  been  ascertained 
to  approximate  VI 2(1.  per  mule  spindle  per  week. 

Thus,  50^  T.  from  double  rove,  and  produced  at  the  rate  of  25*5 
hanks  per  mule  spindle  per  week,  will  cost  in  working  expenses — 

1-72  X  50       „.^_ ,  ^ 

— ^^ —  =  3"37f<.  per  pound 

and  60'  T.  at  23*5  hanks  per  spindle  per  week — 
1-72  X  60 


23-5 


=  A' -id.  per  pound 


The  AppiixiMATE  Cost  of  Yarn   spun   from  Double   Eoving  as  per  Data 

PREVIOUSLY  GIVEN. 


is 

o 

0  -o 

ai 

<U     1 

.3  c 

t-> 

a 

lid 

a, 

a 

cu  . 

t  . 

■"SS 

0     . 

13 

U 

IM    □    ^ 

0  0!  B 

CO  ^ 

0)  0  >> 

12° 

Count  and 

description 

of  yarn. 

5| 

as, 

Suitable  grade  of 
cotton. 

^  .2 
c  a 
o  r:; 

8S 

»*-  o 

o 

a  0. 

2  => 

If 

o2? 
13S-§ 

.£"S 

1  p. 

Jog 

■3-Ss 

0  a;  M 

SI  P. 

9 
1 

CM 

( 

0^ 

°  S 

0  V 

2 

PM 

S^2 

1  G.O.American 

16  \V. 

34 

,  /Broach  G.       > 
*  \Tinnevelly  G. 

5-55 

12 

6-31 

0137 

0-80 

6-978 

1-428 

1 

16  T. 

34 

G,0.  American 

5-71 

12 

6-48 

0142 

0-805 

7-143 

1-433 

16  T.  super. 

33 

8.L.M.       „ 

5-95 

11 

6-68 

0149 

0-83 

7-361 

1-411 

20  T. 

34 

b.L.M.       „ 

6-86 

11 

6-58 

0147 

1-01 

7-443 

1-583 

20  W. 

34 

G.O. 

5-71 

12 

G-48 

0142 

1-01 

7-348 

1-638 

24  T. 

34 

s.L.M.        „ 

5-95 

11 

6-68 

0-149 

1-22 

7-75 

1-8 

24  W. 

34 

f.G.O. 

5-81 

12 

6-6 

0145 

1-22 

7-675 

1-865 

SOT. 

32 

b.M. 

6-05 

11 

6-8 

0151 

1-61 

8-209 

2-209 

SOW. 

32 

s.L.M.        „ 

5-95 

11 

6-68 

0149 

1-61 

8-141 

2-191 

32  T. 

30 

M. 

6-09 

10 

6-77 

0-152 

1-84 

8-458 

2-368 

S6T. 

29 

f.M. 

6-2 

10 

6-9 

0155 

2  35 

9-05 

2-875 

S6  W. 

31 

b.M. 

605 

11 

6-8 

0151 

2-0 

8-65 

2-6 

40  T. 

28-5 

G.M. 

6-31 

10 

7-0 

0-158 

2-41 

9-252 

2-942 

42  W. 

28-5 

s.M. 

615 

10 

6-83 

0-154 

2-53 

9-206 

3-056 

50  T. 

26 

M.F. 

6-55 

10 

7-28 

0-164 

3-31 

10-426 

3-876 

50  W. 

26 

G.M. 

1  Peeler,  Baders,! 

6-31 

10 

7-0 

0-158 

3-31 

10-152 

3-842 

60  T. 

23 

JBoweds,  or  super  > 
I  Orleans  or  Texas) 

— 

10 

— 

— 

— 

— 

60  T.  super 

(  Ditto  (double  j 
\         rove)          j 

American. 

60  W. 

24 

M.F.  American 

6-55 

10 

7-28 

0-164 

4-03 

11-416 

4-866 

50  T. 

25-5 

Egy.  G.F. 

9 

11 

101 

3-37 

0-225 

13-24 

4-24 

50  W. 

26'5 

U.  Egy.  F. 

8/5 

11 

92 

3-25 

0-204 

12-25 

4-07 

60  T. 

23-5 

Egy.  G. 

lOJ 

10 

11-25 

4-4 

0-253 

15-40 

5-27 

60  W. 

25 

U.  Egy.  G.F. 

9fB 

11 

10-3 

4-13 

0-229 

14-20 

5-02 

TOT. 

20-5 

j|Egy-G.      ) 

\i    „      F.G.F./ 

lOi 

10 

11-53 

5-88 

0-259 

17-15 

6-77 

AND   COSTS   OF   YAKN 


235 


■i- 

,      J 

P4 

<a 

*■§ 

•K  3 

5-S 

p<  . 

0.  • 

^8^ 

Count  and 

description 

of  yarn. 

S 

Suitable  grade  of 
cotton. 

as 

•o    . 

§1 

sa 

ble    percentage 
up  to  carding  h 

f  the  cotton  pas 
ding  head  per  po 

ated    value    of 
made  up  to  and 
iided  in  carding. 

S  3 

13 

cost  of  yarn  s 
pence  per  pounc 

n  or  difference 
the  price  of  the 
d  prime  cost  of  y 

1 

s 

II 

Cost  0 
the  car 

Estim 
waste 

cl 

^1 

§-2 

III 

TOW. 

22-5 

U.  Egy.  F.G.F. 

^ 

10 

11-0 

5-35 

0-247 

1610 

6-22 

SOT. 

18-5 

Egy.  G. 

ni 

10 

12-5 

7-44 

0-281 

19-66 

8-41 

SOW. 

19-5 

U.  Egy.  G. 

10^ 

10 

11-36 

7-05 

0-253 

18-16 

6-29 

90  T. 

17-0 

Egy.  F. 

111 

9 

1305 

9-1 

0-297 

21-85 

9-97 

90  W. 

190 

U.  Egy.  F. 

lOi 

10 

114 

8-15 

0-256 

19-30 

905 

100  T. 

15-0 

Egy.  F. 

lOi 

10 

1305 

11-4 

0-297 

24-22 

13-34 

Combed  Qua 

lities 

— 

Cost  of  cot 

at  the  com 

head. 

* 

* 

SOT. 

19 

Egy.  F. 

111 

10+18 

16-4 

/     7-25 
1  +  0-9026 

0  2951 
+1-07  / 

23-1876 

11-3151 

90  T. 

17-5 

" 

Hi 

10+18 

16-4 

f     8-85 
1+0-9026 

0-2951 
+107  / 

24-7876 

12-9151 

100  T. 

16-0 

>» 

Hi 

10+18 

16-4 

/  10-75 
1+0-9026 

0-2951 
+1-07  / 

26-6876 

14-8151 

The  plus  items  in  columns  marked  *  refer  to  the  extra  cost  through  the  combing  pro- 
cess.    The  particulars  of  these  are  given  on  p.  239. 
The  productions  per  spindle  are  given  on  p.  204. 

Costs  of  producing  Yarns  by  Ring  Spinning. — The  cost  of 
preparing  the  cotton  up  to  the  roving  for  ring  spinning  is 
greater  than  for  mules.  In  the  roving  stage  the  cost  is  from 
25  to  33  per  cent,  more  on  account  of  finer  roving  required. 
This  necessitates  more  machinery  for  preparing  the  roving. 
The  costs  of  labour  in  the  spinning  process,  when  producing  the 
classes  of  yarn  for  which  ring  frames  are  most  adapted,  is  in 
some  cases  as  much  as  50  per  cent,  less  than  in  mule  spinning 
process.  Besides  the  extra  preparation,  a  better  class  of  cotton 
has  to  be  used,  and  even  then  the  yarn  is  not  in  a  convenient 
form  for  transport  when  it  leaves  the  spinning  machine.  The  cost 
for  winding  the  yarn  in  a  convenient  form  for  sale  is  consider- 
able.   This  latter  item  is  dealt  with  in  another  part  of  this  work. 

The  following  are  the  yarn  and  cotton  quotations  for 
June  29,  190G.  These  are  given  for  comparison  with  the 
estimated  costs  contained  on  the  foregoing  pages. 


236 


COTTON  SPINNING  CALCULATIONS 


From  the 

"Manchester  Guardian,"  June  30,  1906. 

Good  Bhow- 

nuggar. 
Per  pound. 

20^  water 

twist. 
Per  pound. 

Middling 
American. 
Per  pound. 

32"  cop 

twist. 

Per  pound. 

Fully  good 
fair  Egypt. 
Per  pound. 

60'  twist 

Egypt. 

Per  pound. 

1905. 

d. 

d. 

d. 

d. 

d. 

d. 

September  1 

5 

8i 

5-83 

S^ 

^li 

13| 

8 

4|i 

8i 

5-56 

8i 

7|i 

ISg 

„         15 

4ii 

8i 

5-50 

8i 

7|i 

133 

22 

413 

8i 

5-64 

8i 

7}i 

13i 

29 

4|i 

8i 

574 

8i 

vii 

13i 

October    6 

4U 

8J 

5-41 

8^ 

7}^' 

131 

„        13 

^W 

8 

5-32 

8J 

7}i 

13J 

„       20 

^W 

8J 

5-42 

8J 

7ii 

13i 

,,       27 

m 

8i 

5-71 

Si 

8 

131 

November  3 

4ii 

8i 

5-91 

8i 

81 

131 

10 

4{i 

8^ 

616 

8J 

Si   • 

in 

17 

4}i 

81 

5-93 

8| 

81 

14J 

2i 

4{i 

SI 

611 

9 

81 

14J 

December  1 

4i 

m 

616 

81 

81 

141 

8 

5 

9 

6-42 

9^ 

8ft 

14i 

15 

47 

8? 

6-29 

% 

81 

14i 

„         22 

4}i 

8f 

6-31 

9 

81 

141 

29 

H 

8U 

6-24 

9 

81 

141 

1906. 

January    5 

Iji 

81 

6-23 

9 

8k 

141 

12 

^ 

81 

6-09 

m 

8tI 

141 

„        19 

4| 

8i 

6-30 

»i 

81 

141 

„        26 

4|i 

8i 

612 

8f 

8i 

14i 

February    2 

^ 

8i 

5-99 

8i 

8?, 

14| 

9 

45 

8.1 

5-87 

8i 

8\h 

15J 

16 

^ 

8i 

5-91 

8i 

81 

15i 

23 

4| 

8i 

5-73 

81 

81 

15i 

March    2 

41 

8,^B 

5-78 

8i 

9V8 

15i 

9 

^ 

8t*8 

5-92 

8| 

9| 

151 

„      16 

^ 

8t^s 

5-77 

81 

91 

15i 

„      23 

n 

8.1 

5-84 

81 

9,'b 

16^ 

„      30 

n 

8i 

6-03 

8| 

91 

15i 

April    6 

41i 

81 

6-10 

9 

91i 

161 

„     12 

4{i 

8i 

6-16 

9| 

101 

i6i 

»     20 

4U 

81 

604 

9^ 

lOi 

16i 

„     27 

4^ 

8}^ 

607 

9J 

lOi 

16i 

May    4 

m 

8? 

608 

9 

101 

16i 

„     11 

43 

8| 

6-18 

9J 

101 

16i 

„     18 

4i 

8Ji 

6-25 

% 

101 

i6i 

„     25 

43 

8? 

6-20 

91 

101 

i«i 

June    1 

4^4 

8? 

602 

91 

10| 

16i 

»       8 

41^ 

8| 

601 

91 

10| 

16i 

„      15 

4|^ 

8| 

607 

9i 

101 

16^ 

„      22 

^ 

8^ 

612 

n 

IOi'b 

16^ 

„      29 

^ 

8:1 

610 

9i 

lOi 

16J 

AND   COSTS   OF  YAEN 


237 


From  the  "Cotton  Factory  Times,"  June  29,  1906. 

PRICE   of   medium   tarns   IN   PENCE   PER   LB. 


Count. 


4-16 
10-28 

20 

30 

32 

36 

34 

40 

50 

60 

70 

80 


AVeft. 


8-9 

013_Q  9 

9i'6-9H 

9^6-10 

12|-13| 
14-15 

17H8i 


Twist  in  cop.  gea^j. 


^T6    ^'iS 


9TV10i 


9ft 
12^ 


-lOi 
-llf 
-13i 


Bundle. 


8F9i 
9=1-10' 


lOJ-lll 
llM2i 


1                 Twofold. 

Bundle. 

Cop. 

— 

— 

9H0i 

9f'B-10^ 

loi-iii 

10tV"t^b 

11H2^ 

lli-12i 

Uf^li 

13^131 

— 



EGYPTIAN   YARNS. 


60 

15A-1G^ 

— 

— 



171-21 

17i  -20^ 

70 

16H7i 

—                  — 

— 

19i-24 

19I-23J 

80 

171 -18i 

—                  — 

— 

21i-26f 

211-26^ 

90 

18i-20i 

— 

— 

— 

23^-30 

23^29^ 

100 

20i-22J 

— 

25H3i 

25i-32i 

Cotton,  Official  Quotations. 
June  29,  1906. 


American 


G.o. 
5-73 


American. 
L.M.  Md. 

5-93  611 


G.M. 
G-33 


F.G.M. 
6-43 


M.F. 
6-61 


M.F. 

Fair. 

G.F. 

Pemain 

Ceara 

Paraiba 

Maceio 

5-78 

5-85 

5-77 

*o-79 

618 
6-23 
615 

*6-17 

6-44 

6-45 

6-39 

*6-39 

Fair. 

Egyptian. 

G.F. 

F.G.F. 

Gd. 

Egyptian,  brown      .     . 
Ditto,  upper   .     .     .     . 

!           8? 

91 
8}i 

lOi 

9e 

*9i 

Egyptian,  brown,  fine,  11^. 

Ditto,  upper,  fine,  *10. 

Egyptian  quotations  do  not  refer  to  Bamia  or  Upper  Egypt  cotton. 


Nominal. 


238 


COTTON   SPINNING  CALCULATIONS 


Tnd 

ian. 

F.F. 

G.F. 

F.G.F. 

Gd. 

F.G. 

Fine. 

Broach      .... 

_ 

_ 

5i 

5U 

5Vb 

Bhownuggar .     .     . 

— 

*4i 

*ik 

*4i 

*43 

HI 

No.  1  Oomra .     .     . 

— 

*n 

*41 

*4| 

*43 

HI 

Bengal 

— 

m 

Q2S 
^35 

3§i 

ii. 

i^% 

Tinnivelly     .     .     . 

— 

5A 

K3 
^8 

5^ 

— 

Bengal,  Superfine,  4|. 


*  Nominal. 

The  Costs  of  Power  available  at  the  Machines,  in  a  Spinning  Mill. 

Basis :  EDgine  and  all  plant  connected  therewith  to  develop 
1000  I.H.P. 

Engines,  boilers,  and  economizers  —  Pumps  and  all  the 
necessary  connections — Shafting  and  rope-gearing — Keservoirs, 
land,  buildings,  and  approaches  at  £15  per  I.H.P.  =  ^£15,000. 

Piatio  of  above  costs — 

(a)  Engines,  35  per  cent. 

(b)  Boilers  and  economizers,  20  per  cent. 

(c)  Shafting  and  rope-gearing,  15  per  cent. 

(d)  Reservoirs,  land,  buildings,  and  approaches,  30  per  cent. 

Woi'king  Expenses ; —  £        «.     d. 

Depreciation  and  upkeep  inclusive  on  (a),  {b),  (c),  at  10 

per  cent,  per  annum 1050  0  0 

Depreciation  and  upkeep  on  (fZ),  at  2i  per  cent.     ...  112  10  0 

Interest  at  4  per  cent,  per  annum  on  (a),  (b),  (c),  {d)  .     .  600  0  0 

Stores  at  £0*25  per  I.H.P.  per  annum 250  0  0 

Coals  :  2  lbs.  per  I.H.P.  per  hour,  at  7s.  Qd.  per  ton    .     .  1 47G  0  0 

Insurance  (fire,  accident),  at  10s.  per  cent,  on  £12,000  .  60  0  0 

Labour 400  0  0 


3948  10    0 


Cost  per  I.H.P.  per  hour  in  pence  (50  X  55  working  hours) — 

3948-5  X  240 
50  X  55  X  1000 

The   inclusive   j)ower   required  in  spinning  mills,  is  about 


AND   COSTS   OF   YARN  239 

1  I.H.P.  per  63  spinning  spindles  in  mills  containing  all  mule 
spmdles,  and  about  1  I.H.P.  per  44  spinning  spindles  in  mills 
contammg  all  ring  spinning  spindles. 

The  power  required  to  drive  the  various  machines- 
Hopper  cotton  pullers  and  feeders .     .     1    LHP.  per  machine 
Simple  Creighton  opener 2^ 

ylfW ;  For  each  extra  cylinder  or  beater     2 
For  each  lap  machine  .     .  2 

Jb  or  automatic  feeders  .  l 

T7I  •  •         •         •         -^  J)  ,, 

i^  or  pneumatic  cleaning  trunks.  1^ 
Other  types  of  openers  as  above. 
Scutchers,  single  with  lap  machine     .31 

Cards -^~ 

Sliver  lap Q.g 

Eibbon  lap I'O      ' 

Comber,  per  combing  head    ....  01 

Drawing  frames,  5  dels,  per  ....  1 

Slubbing  frames,  45  spindles  per  .     .  1 

Intermediate  frames,  60  spindles  per  .  1        '^ 

Eoving  and  ring  frames,  80  spindles  per  1 

Mules,  110-120  spindles  per  ....  1        '| 

The  Cost  of  Spaces  in  Spinning  MiUs.-This  works  out  at  about 
2s.  per  square  yard  per  annum,  inclusive  of  lighting  and  rates 

The  Extra  Cost  when  the  Process  of  Combing  is  introduced.— 
The  productive  capacity  of  a  machine  of  the  Heilmann  type,  as 
made  by  the  principal  makers,  ranges  from  300  to  500  lbs.  per 
machine  of  eight  heads. 

In  the  following  estimate  moderate  working  conditions  have 
been  assumed,  the  production  being  taken  at  400  lbs.  per  week 
of  551  hours  per  machine,  and  the  waste  extracted  at  18  per  cent. 

The  quantity  of  cotton  required  for  treatment  would  there- 
in      ,     400  X  100 
fore  be  ^ —    =  488  lbs. 

Assuming  a  wastage  of  2^  per  cent,  between  the  combing 
and  carding  stages,  the  amount  of  carded  cotton  required  per 
400  lbs.  of  combed  would  be  500  lbs.     If  a  loss  of  5  per  cent  is 


240  COTTON   SPINNING  CALCULATIONS 

allowed   for   in  the    card,  then  '^ — ^  - —  =  weight  of  cotton 

required  in  card  laps,  527  lbs. 

And  if  5  per  cent,  loss  be  allowed  for  in  opening  and  scutch- 

,,        527x100      ^^^,,        ,  ,,  .     ,         ,^^„ 

mg,  then, ~ =  555  lbs.  of  raw  cotton  required  per  400  lbs. 

of  combed  cotton. 

When  combing  is  not  in  vogue  this  amount  would  be  less 
to  the  extent  of 

.^.      /400  X  100  X  100\      ^^.       ,,.       ,,,  „ 

Assuming  the  production  of  the  card  350  lbs.  per  week,  the 
extra  carding  machinery  per  400  lbs.  of  combed  sliver  would  be— 

(500  -  400  =  100  lbs.)  =  ^^ 

Taking  the  productive  capacity  of  a  scutcher  at  8000  lbs.,  and 
that  of  the  opener  at  16,000  lbs.  per  week,  respectively,  the  loss 
being  2  and  3  per  cent,  respectively,  then  the  extra  scutching 
and  opening  machinery  would  be — 

106  .         109 

scutchmg,gQQQ;  opening,  jg^ 

The  extra  labour  involved,  upon  the  following  basis,  would 
cost  as  follows  : — 

Cost  of  treating  16,000  lbs.  of  scutched  cotton. 

Mixing,  opening  and  scutching,  wages  inclusive,  £3  15s. 

The  cost,  therefore,  of  treating  the  extra  cotton  required  (106 
lbs.  scutcher  lap)  would  be — 

3-75  X  240  X  106  _  .  q  , 
16000  ~  ^*^''- 

Therefore  the  extra  cost  on  account  of  labour  under  this  head 
would  be — 

5*9 

Tjrx  =  0"01475(7.  per  pounds  of  combed  cotton 


AND   COSTS   OF   YARN  241 

Taking  the  labour  in  carding  at  28s.  per  14  cards  inclusive, 
the  cost  per  pound  of  combed  sliver  would  be — 

—- — -^^  =  0*01701(?.  per  pound  of  combed  sliver 

350  X  14  X  400  ^     ^ 

The  costs  of  labour  involved  in  preparing  the  cotton  for  and 
in  combing : 

One  person,  at  18s.  per  week,  to  attend  the  sliver  and  ribbon 
lap  machines.     Production,  2450  lbs.  per  week. 

— r— — -^^ — -~r—  =  0108fL  per  pound  of  combed  cotton 
2450  X  400  ^      ^ 

One  person,  at  20s.,  per  six  combing  machines  inclusive  of 
cost  of  overlooking — 

20  X  12 

n 77^  =  O'l^^-  per  pound  of  combed  sliver 

b  X  400  ^      ^ 

Other  expenses  : 

Costs  on  account  of  the  machinery — 

Approsimate    Proportional  cost 
coat.  per  combing 

machine. 
£  £ 

Cotton  puller 140  0*92 

Opener 300  1-97 

Scutcher 180  2-36 

Card 100  28-6 

Silver  lap 60  12-0 

Kibbon  lap 140  28-0 

Comber 170  170*0 

Total    .     .     .     £243-85 

Eepair  and  upkeep  at  Ti  per  cent,  per  annum  oii\  _  n-,Q  o 
£243-85  ~  j  -  ^1«'289 

Depreciation  at  7i  per  cent,  per  annum  on  £243*85  =     18'289 
Interest  at  5  per  cent,  per  annum  on  £243*85     .     .  =     12192 

£48-770 
Cost,  under  this  head,  per  pound  of  "1       48-77  x  240 


I  =  Z^\/\"r  =  0-585^/. 


combed  sliver  j         50  X  400 


242  COTTON  SPINNING  CALCULATIONS 

Extra  stock  of  cotton  in  process  through  combing,  say  400 
lbs.  per  combing  machine  of  8  heads. 
Value  of  this  at  8d  per  lb.  =  £13-3. 

Interest  on  £13'3  at  5  per  cent,  per  annum  =  £0'665 

Therefore  cost  per  pound  of  combed  sliver  =  --^ 77-^-  =  0-008 

^     ^  50  X  400 

Extra  cost  on  account  of  space,  at  2s.  per  square  yard  per 
annum — 

Proportional  area  : 
square  yards. 

Space  per  combing  machine  (400  lbs.),  15  square  yards  =  15-0 
ribbon  lap      ,,     (2450  lbs.),  15  „  =    2*5 

sliver  „  12  „  =2-0 

19-5 

19"5  X  2  X  12 

Cost  per  pound  of  combed  sliver  =  — -7^ ,^^      =  0*0234f/. 

^      '-  50  X  400 

Extra  cost  on  account  of  power,  at  0"344(/.  per  I.H.P.  per 
hour — 

Proportional 
power. 

Comber  (400  lbs.) |  I.H.P.       0-75 

Eibbon  lap  machine  (2450  lbs.)     1      ,,      ^ 
Sliver  „  ,,  h      „      f 

The  extra  cost  on  account  of  the  waste  extracted — 

Waste  at  the  combing  stage,  88  lbs. 

Extra  waste  at  the  previous  stage,  not  returnable  to  mixing, 
555  -  444  =  111  lbs. 

Therefore  111  +  400  =  511  lbs.  the  amount  of  raw  cotton 
required  per  400  lbs.  combed,  and  therefore  the  cost  of  the 
cotton  per  pound  at  the  combing  head  on  this  account  is — 

Sd.  X  511 


400 


=  10'22(^?.  per  pound 


AND   COSTS   OF    YARN  24 

Summary  of  Costs. 

Per  pound  of 
combed  sliver. 

Labour  :  On  account  of  extra  mixing,  opening,  and  scutching  .  0'01475 

carding 0-01715 

„         Preparing  the  comber  lap 0"108 

„         Combing 0*1 

Machinery  and  upkeep,  repairs,  and  stores 0'585 

Extra  stock  of  cotton 0-008 

Space 0-0234 

Power 0-0473 


Tlie  total  expenses  nominally  unaffected  by  changes  in  cotton 

values 0-9026 

Value  of  the  cotton  at  the  combing  head 10-22 


11-1226 
Cost  of  raw  cotton 8-0 


Extra  cost  of  combing  (value  of  the  waste  reserved)    ....       3-1226 
Allow  for  value  of  the  waste I'O 


Nett  extra  cost  of  combing 2-1226 

80^ — The  cost  of  combing,  when  the  raw  cotton  costs  11,^':/. 
per  pound  and  the  waste  at  this  stage  is  18  per  cent.,  and 
10  per  cent,  previous,  allowing  50  per  cent,  of  the  cotton  value 
for  comber  waste  sold — 

11"(/ 
Value  of  the  waste  =  18  per  cent.  1  lb.  at  — ^'  =  1'07(/.  per  pound 

The  extra  waste  made  in  scutching  and  carding  will  be 
worth  about  2.}  per  cent,  of  the  cotton  price  per  pound — 

The  cost  of  the  cotton  at  the  combing  head  is  therefore 
HZ  X  100 


72 


=  16-4(?. 


The  cost  of  spinning  80'  uncombed  on  the  basis  of  19  hanks 
produced  per  spindle  (see  p.  235) — 


244  COTTON   SPINNING  CALCULATIONS 

1-72  X  80      _.,,., 

The  other  expenses  of  combing — 

0-9026fL  per  pound 

Hence,  assuming  the  waste  made  at  the  comber  is  sold  at  a 
price  per  pound  equal  to  half  the  cost  price  of  the  raw  cotton, 
then  the  extra  cost  of  combing  in  this  case  would  be — 

18  per  cent.,  1  lb.  x  'Tjd.  =  0'T2d. 

The  cost  of  combing  =  11-1226  -  B'O  -  072  =  2-5026(/. 

per  pound 11*1226 

10-22 


The  expenses  exclusive  of  the  loss  in  waste    ....    0"9026(Z. 


10-22 
8-0 


The  cost  on  account  of  the  waste  extracted,  assuming 

it  has  no  value 2*22 

Costs  of  80'  combed  as  per  tabulated  data  on  p.  235.  The 
cost  of  combing  and  spinning  when  the  raw  cotton  costs  llld. 
per  pound. 

The  cost  of  spinning  (uncombed)  as  per  tabulated  data  on 
p.  235— 

1-72  X  80         _^- „         „      , 
— =     7  25  per  lb.  of  yarn 

The  cost  of  the  cotton  at  the  combing\ 

head,  through  waste  loss,  neglect-[=   16-4  ,,         ,, 

ing  value  derived  from  sale  ] 

The  expenses   of  combing,   excluding]         aoaoa 

waste  f-     ^"^^^^      "         " 


AND   COSTS   OF   YAEN  245 

Less  the  value  of  18  per  cent,  waste) 

made  in  combing  (at  half  price  of  =  -1-07  per  lb.  of  yarn. 

raw  cotton  per  pound)  I 

Less  the  value  of  waste  made  prior  to ) 

combing   (at   2^  per  cent,  on   the   = -0-295 

raw  cotton  price)  J  "         »» 

Cost  per  pound  of  yarn  =  231876f?. 
Example  of  the  method  adopted  in  estimating  the  cost  given  below- 
Cardincj  :  850  lbs.  per  card — 

Cost  per  pound 

Labour:  2s.  lid  per  card,  inchisive  of  over-  .s.  d.  y'^"'"*!'""- 

looking  and  card  head  tenter 2  11  =  0-043-^ 

Power:  1  H.P.  per  card  at  0-34rZ.  per  hour     .  1  GT  =  O-Q-^-^O 

Machinery:  £100  per  card,  10  per  cent,  for 

loss,  depreciation,  and  upkeep 4  1  =  0-057G 

Space  :   10-58  square  yards  per  card  at  2s.  per 

y^'"^ 0  5-18  =0-0061 

8  11-88        0-1289 

The  cost  at  the  drawing  and  subsequent  stages  is  given  per 
productive  unit,  on  account  of  the  wide  range  of  variation  in 
then-  production.  In  order,  therefore,  to  estimate  the  cost  per 
pound,  the  production  per  delivery  or  per  spindle  is  required. 
The  production  can  be  ascertained  in  the  manner  explained  in 
other  parts  of  this  book. 

The  Departmental  Costs  in  Spinning  Carded  aualities  of  Yarn  — 
In  estimating  these  costs  up-to-date  conditions  have  been  taken 
as  the  basis.  The  cost  of  space  has  been  assessed  at  2s.  per 
square  yard  per  annum,  inclusive.  But  no  allowance  has  been 
made  for  waste. 


Mixhuj-Cotton  and  W.ufe  Stormje-Openh.g—ScutcU 


ruj- 


Cost  in  pence  por  pound 
T    ,  of  yarn  spun. 

L'-ibonr ^,^^^ 

l^'^f. 0-0255 

^^^^^^'"^^•y 0-0144 

^"^^^^ 0-00317 

0-07007 


246  COTTON   SPIKXIXG   CALCULATIONS 

Carding — 

Cost  in  pence  per 
card  per  week. 

Labour 35'0 

Power 18-7 

Machinery 49-0 

Space 5'18 

107-88 
Drawing — 

Cost  in  pence  per 
delivery  per  week. 

Labour 12'5 

Power 3'75 

Machinery 16-0 

Space 0-7G 


0. 9,. 


01 


Fly  Frames  : 

Sluhber — 

Cost  in  pence  per 
spindle  per  week. 

Labour 3'25 

Power 0-415 

Machinery 0-87 

Space 0-195 

4-730 
Intermediate — 

Labour 1-75 

Power 0-31 

Machinery 0-575 

Space 01 

2-735 
Roving — 

Labour 0-88 

Power 0-268 

Machinery 0-4 

Space     . " 0-067 

1-615 
Mules — 

Labour 0-45 

Power 0-156 

Machinery 0-15 

Space 0075 

0-831 


AND   COSTS   OF    YARN  247 

Rings — 

Cost  in  pence  per 
ppindle  per  week. 

Labour 0*25 

Power 0-235 

Machinery 0-216 

Space 0-029 

0-730 
Twining — 

Labour 0-66 

Power 0-113 

Machinery 0-12 

Space 0-067 

0-960 

In  twining  the  waste  and  costs  of  steaming  and  unpacking 
and  packing  the  yarn  must  be  added. 

The  waste  is  sometimes  a  considerable  addition  to  the  cost. 

Twice  the  labour  cost  should  always  more  than  cover  all 
expenses. 

Ring  Doubling — 

Cost  in  pence  per 
spindle  per  week. 

Labour 0-5 

Power 0-312 

Machinery 0-25 

Space 0-044 

1-106 

Other  expenses — namely,  waste,  travellers,  grease,  spindle 
banding,  bobbins — are  considerable.  The  "waste"  should 
always  be  considered  as  a  separate  item ;  0*25  is  a  reasonable 
allowance  for  the  rest. 

Doubling  Winding,  or  Winding.— The  production  per  spindle 
is  considered  good  at  75  per  cent,  of  the  calculated  without 
allowances. 

The  number  of  spindles  attended  by  one  person  may  be 
estimated  from  the  rate  the  winder  can  piece  up  as  follows: 
Assume  the  winder  can  piece  up  at  the  average  rate  of  12 
ends  per  minute,  and  that  in  the  course  of  unwinding  each 
ring  bobbin  end  breaks  twice,  allowing  25  per  cent,  for  the 
spindles  stopped  through  incidental  breakages. 


248  COTTON    SPINNING   CALCULATIONS 

On  this  assumption  the  production  per  winder  will  be — 

55  hrs.  X  60  mins.  x  12  x  ounces  contained  on  each  bobbin 

2  X  16 
=  pounds  per  winder 

Number  of  spindles  per  winder 

_  pounds  per  winder  j_  ok 

~  75  per  cent,  calculated  production  per  spindle  ^ 

A  Method  of  Ascertaining  the  Production  of  Reels. — The  pro- 
duction of  40-hank  reels  in  55  hours  when  worked  at  250 
revolutions  of  the  swift  per  minute,  allowing  two  stops  per 
bobbin  unwound,  and  5  seconds  for  each  stop,  the  bobbins 
containing  0*75  oz.  of  counts  20^  the  time  lost  in  tying  and 
doffing  being  3  minutes. 

The  time  taken  to  fill  the  reel  (40  hanks)  if  no  stoppages 

80  X  7  X  60 

= ?r^rpr seconds 

ZoO 

The  number  of  stops  in  filling  the  reel 

840 


0-75 

^  X  840  X  20 
lb 


X  2 


The  time  lost  in  filling  the  reel  through  stopping 
840 


^  X  840  X  20 
lb 


X  2  X  5  X  40  seconds 


The  time  taken  to  fill  and  doff,  allowing  two  stoppages  per 
bobbin  unwound 

^  80  X  7  X  60      840x16x2x5  xJO 

250         "^        0-75x840x20        +  ^^^ 
=  134-4  +  427  +  180  seconds  =  12-37  minutes 

The  production  per  week  in  pounds 

55  X  60      ,       _„^  ,, 


AND  COSTS   OF   YARN  249 

The  weekly  earnings  of  winders  and  reelers  vary  from  14.s. 
to  24s.  per  week,  and  the  cost  per  pound  of  yarn  treated, 
varies,  in  this  work,  comparing  districts,  more  than  in  any 
other  section  of  the  spinning  mill. 

The  numerous  departmental  wage  lists  and  the  difference 
in  these,  in  the  various  districts,  do  not  admit  of  the  costs  in 
wages  being  treated,  in  a  work  of  this  kind,  in  any  other  manner 
than  that  adopted. 

Although  these  lists  differ  on  paper,  competition  has  resulted 
in  this  difference  in  the  costs— being  that  approaching  the 
vanishing  point,  when  reduced  to  a  basis  embodying  quantity 
and  quality  of  production. 


INDEX 


Attenuation.    See  Draft 

Backing-off  and  taking-in  motion,  157, 

IGO,  178 
Bale  breakers  or  cotton  pullers,  15-25 

gearing  in,  15,  21 

hopper  type  of,  15,  21-25 

Belt  and  rope  driving,  12 

Brooks  and  Shaw's  type  of  differential 

(slubber  frame),  138-140 
Builder  wheel  in  mule,  168 

ascertaining     suitable,     in 

changing  counts,  168 

changes  in,  168 

in  ring  frame,  210 

Building  motion,  159, 178 

Card  calculations,  56 

conditions  controlling  output  of,  G6 

Carding     department,     proportions    of 

machinery  in,  141 

parts,  conditions  respecting  actions 

of,  G(J 

functions  of  lickerin,  cylinder, 

flats,  doffer,  66-68 
Combing  machines,  84-101 

detaching  rollers,  87 

drafts  in,  89,  97 

adjustment  in,  99 

lap  rollers,  87 

Nasmith  and  Heilmann  ma- 
chines compared,  95 

Nasmith's,  gearing  in,  84-8(5, 

95-97 

productive,  93 

Cone  drums,  use  of,  in  fly  frames,  126 
Constants  for  twist — 

normal,  for  roving,  111,  112 

standards  for  single  yarn,  161,  214 

for  folded  yarn,  216 

crochet,  217 

fish  netting,  217 

knitting   yarns  and    embroidery,  and 
for  mercerizing,  217 

sewings,  217 
Costs  of  yarn,  231-247 

by  mule  spinning,  231 

by  ring  spinning,  235 


Cost  of  yarn  extra  when  combing  intro- 
duced, 239 

departmental,  249 

winding  and  reeling,  247,  248 

of  power  available  in  mills,  288 

of  space  in  spinning  mills,  209 

Cotton,  names  applied  to.  in  its  prepara- 
tion, 71 

system  of  counting,  in  its  stages  of 

preparation,  71 

Cotton  pullers  or  bale  breakers,  15-25 

gearing  in,  15,  21 

■ hopper  machine,  15,  21-25 

Count,  71,  117 

changes  in,  in  mule,  157 

~ in  ring  frame,  209 

of  laps  made  by  openers  and 

scutchers,  52 

— —  changing,  ascertaining  suitable 
building  wheel  in,  168 

of  intermediate  roving,  150 

of  sliver  at  the  drawing  frame,  151 

of  slubbing  rove,  150 

Counting  cotton,  system  of,  71.  See  aho 
Count 

Curtis  and  Rhodes  type  of  differential 
(roving  frame),  129 

Differentials,  principal  types  of,  127-140 
Brooks  and    Shaw's  (slubber 

frame),  138-140 
Curtis    and    Rhodes    (roving 

frame),  129 

Fallows      motion     (slubbing 

frame),  135 
Tweedale  (intermediate  frame), 

133 

use  of,  in  fly  frames,  120 

Dobson's  ord.  mule,  177 

gearing  in,  177,  195 

double-speed  and  hastening  motion, 

190 
Draft,  19,  35 

between  various  parts,  how  ascer- 
tained, 62 

how  altered,  64,  65 

changes  in  total,  69 

in  combing  machines,  89,  97 


252 


INDEX 


Draft  in  drawing  frames,  103,  107,  109 

iu  fl}-  frames,  142,  151  i 

in  mules,  157 

in  openers,  3i-40  ' 

in  ribbon  lap  machines,  82 

in  ring  frames,  209 

in  scutchers,  43-47  ] 

in  shver  lap  machines,  78 

Drawing  frame,  102 

calculations  relating  to,  103 

coiling  of  sliver,  spacing,  105 

count  of  sliver  at,  151 

drafts,  103,  107,  109 

effect  of  atmospheric  changes, 

102 

system  of  gearing  rollers,  108 

rollers,  analysis  of  action  of,  152 

functions  of,  153 

I)river  and    driven    wheels,    eflect    of 

chaoging,  9,  10 
Driving,  rope  and  belt,  12 

speeds  and   sizes  of  driving 

surfaces,  12-15 

Equilibrium,  state  of,  in  yarn,  223 

Fallows  t\'pe  of  differential  (slubbiug 
frame),  135 

Fillet,  length  and  preparation  of,  re- 
quired to  cloth  cylindrical  surface,  75 

Flats,  in  cards,  functions  of,  67 

rate  of  movement  of,  67 

Fly  frames,  110-152 

■ — consequences  of  altering  value 

of  cone  train,  114 

cone  drums,  use  of,  126 

count,  150,  151 

changes  in.  118 

draft,  142,151 

alterations  in,  117,  118. 

119 

dififerentials,  principal  tvpes 

of,  127-140 

use  of,  12G 

drawing    rollers,    action     of, 

analysis,  152 

gearing  in,  112-115 

hank  indicators,  154 

"  preparations,"  141 

■ processes,  three  stages,  141 

■ production  in,  145 

rate  of  winding  and  spacing 

of  coils,  120 

speed  of  spindles,  149 

speeds,  115,  140 

twist  constants,  111 

twisting  in,  object  of.  Ill 

winding  in,  obtained  bv  bob- 
bin, 125 


Gain,  or  drag,  161,  164 

changes,  166,  186 

Gearing  iu  bale  breakers,  15,  21 

in  carding  machines,  56 

in     Dobson's    double-speed     and 

hastening  motion,  190 

in  draw  frames,  103 

in  fly  frames,  112 

in  mules,  156 

— — Dobson    and   Barlow's,  177, 

195 

Piatt's,  183,  191, 192 

various  trains,  162,  177-190 

in  Nasmith  combing  machine,  84 

iu  openers,  25 

in  Piatt's  knocking-off  motion,  51 

in  ribbon  lap  machines,  SO 

in  ring  frames,  204 

doubling  frames,  224 

rollers,  108 

in  scutchers,  41 

in  sliver  lap  machines,  76 

in  twiner  mule,  228 

various  trains  of,  calculations  and 

other  particulars  of.  161-177 

Half-lap,  75 

preparing,  75 

Hank  indicators,  154,  200-203 
Hastening  motion,  161 

Dobson's,  190 

Hetherington  mule,  162 

Hopper  type  of  cotton  puller,  21-25 

gearing  in,  21 

usefulness  of,  24 

Hunting     cog     measuring    or    length 

motion,  used  in  openers  and  scutchers. 

48 
advantage  of,  50 

Indicators,  hank,  for  frames  and  mules, 
158,200-203 

length,  200 

speed,  their  use,  198 

Jacking  or  ratching  motion,  158.  162 

Piatt's,  191 

t   Trelfall'e,  193 

'   Knocking-off  motion  in  scutchers,  Piatt's, 

I       ^^ 

Laps,  71 

i  changes  in  weight  and   count  of, 

made  by  openers  and  scutchers, 
52 

'   length  of,  49-51 

rollers,  87 

Length  and  hank  indicators,  200-203 
1  stop  motion,  150 


INDEX 


253 


Motiou,  rate  of,  calculating,  when  tooth- 
gear  employed,  1 

transmission  of,  1-15 

Motions — 

backiug-oflf  and   takini'-in,  157,    1(J0 
178 

building,  159,  178 

double-speed,  159,  19U 

hastening,  161,  190 

jacking  or  ratching,  158,  162,  191,  193 

knocking-off,  51 

length  stop  or  full  bobbin,  156 

receding,  158,  178 

roller  delivery,  160 

twisting,  159 
Movement  of  tooth  wheels,  direction  of, 

Mules,  156-204 

calculations,  156,  183 

compared  with  ring  frame,  213 

costs  of  yarn,  231 

counts,  changes  in,  157 

drafts  in,  157 

Dobson's  and  Barlow's,  177,190,  194 

gearing  in,  150 

various  trains  of,  162-167 

Hetheriugton,  162 

losses  in  driving  in,  194,  196 

motions,  157-161 

Piatt's,  183,  191, 192 

productions  in,  204 

proportion  of  machinery  forming  a 

"preparation,"  142 

Trelfall's,  193 

twiner,  228-230 

twist  per  inch,  197 

wheel  train  values  in,  conditions 

governing  changes  in,  161 

various,    and    range    in 

size  of  wheels,  177-190 

Openers,  15-40,  48-56 

changes  in   weight   and   count  of 

laps  made  by,  52 

drafts  in,  34-40 

gearing  in,  25 

hunting  cog  measuring  or  length 

motion  used  in,  48 
productions,  speeds,  and  controlling 

factors,  54 
Overscutching,  55 

Piatt,  Bros.,  jacking  motion,  191 
Piatt's  knocking-off  motion,  51 

■ gearing  in,  51 

Plucking  from  feed  rollers,  54 

"Preparation,"  70,  141 

proportion  of  machinery  forming  a, 

in  mule  spinning  and  ring  frame 

spinning,  142 


Productions,  and  their  controllintr  fac 
tors,  53,  54 


Keceding  motion,  158,  178 
Revolution  of  wheels,  law,  1 
Ribbon  lap  machines,  80 

drafts  in,  82 

— ; production  in,  83 

Ring  doubling  frames,  224-228 

gearing  in,  224 

production  in,  226 

slippage  in,  228 

twist  obtained,  224 

■ winding,  247 

Ring  frames,  204-224 

builder  wheel  (ratchet),  210 

compared  with  mule,  213 

costs  of  yarn,  235 

counts,  changing,  209 

gearing  in,  204 

looses    in    driving    spindles, 

212 

productions  in,  213 

proportion  of  machinery  form- 
ing a  "  preparation  "  in,  142 

speeds  of  spindles,  206,  212 

twist  per  inch,  207 

Ring  spinning.     See  Ring  frames 
Roller  delivery  motion,  160 
Rope  and  belt  driving,  12 

calculating  speeds  and  sizes 

of  driving  surfaces,  12-15 
Rotation,  direction  of,  6 
of  wheels  in  any  direct  train,  rela- 
tive rates  of,  law,  3 


Scutchers,  41-56 

changes  in   weight   and   count   of 

laps  made  by,  52 

draft  in,  43-47 

gearing  in,  41-43 

hunting  cog  measuring  or  length 

motion  used  in,  48  ^ 

particulars  of  driving,  41 

productions,  speeds,  and  controlling 

factors,  54 
Sliver,  or  web,  65,  71 

coiling  of,  105 

■;;-;—  weight  of  the  card,  152 
Sliver  lap  machines,  76 

drafts  in,  78 

production  in,  79 

• to  alter,  79 

Speed  indicators,  198 
Speeds  in  scutchers  and  their  control- 
ling factors,  53,  54 

altering,  61 

Stop  motions,  length.  156 


254 


INDEX 


Tachometer,  the,  198,  199 
Tooth-gear,  calculatiug  rale  of  motion 
wlien,  employed,  1 

wheels,  direction  of  movement  of,  2 

Transmission  of  motion,  1-15 
Trelfall's  jacking  motion,  19:> 
Tweedale   type    of   differential    (later- 
mediate  frame),  133 
Twiner  mule,  228-230 

gearing  in,  228 

Twist,   constants,    for    roving,   normal, 
111,  112 

standards    for    single    yarns, 

161,214 

■ doubling,  aims  and  effects  of,  220 

constants  used  in,  216 

in  roving  direction  and  usefulness, 

111 

effects  of.  211 

in  single  yarns.  21.3 

influence  of  direction  of,  in  folded 

yarns,  218 

object  of,  111,  2U1 

obtained  in  ring  doubling  frames, 

224 

per  inch  and  per  draw,  197 

in  ring  frames,  207 

relative  resistance  of  yams  to,  222 

■ standards,  for  folded  yarns,  216 

for  6in,(,'le  yarns,  214 

state  of  equilibrium,  223 

influence  ou breaking  strength,  215, 

216 
twisting    two     or     more    threads 

together,  219 


Wheel  trains,  4-11 

calculating  value  of,  8 

direct  and  indirect,  4-6 

effects  of  changing  wheels,  9 

values  of,  in  mules,  conditions 

governing  changes  in,  161 

various,  particulars  of,  177 

See  Gearing 

Wheels,  classification  of :  driver,  driven, 

carrier,  6 

direction  of  rotation,  6 

effects  of  changing,  9 

law  of  revolution,  1 

relative  rates  of  rotation,  3 

Winding  in   fly   frames,  how  obtained, 

125 
Wrapping,  70 


Yarn,  71 

costs  of  (q.v.),  231-247 

doubling,  aims  and  effects  of,  220 

folded,  twist  standards  for,  216 

influence  of  direction  of  twist 

on  strength  of,  218 
relative    resistance     of,    to    twist, 

222 

singli',  twist  standards  for,  214 

. effects  of  twist  in,  214,  215 

state  of  equilibrium,  223 

t'ltal    length    of.  per    draw,   197, 

2J3 

testing  for  breaking  strength,  215, 

216 


».©• 


THE    END 


'^B  ~  "»- 


FSIKTED   Br   WILLIAM   CLOWES  ASD  SOKS,   LIMITED,   LOKDOX   AKD  BECCLES. 


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